PAPA
Modeling the stylized facts
of wholesale system marginal price (SMP)
and the impacts of regulatory reforms
on the Greek Electricity Market
George P. Papaioannou a, PhD,
Panagiotis G. Papaioannou b
Nikos Parliarisc, MSc
a Center
for Research and Applications of Nonlinear Systems, CRANS,
University of Patras Greece (Adjunct Researcher) and
ADMIE S.A., the Independent Power Transmission Operator, Greece.
b National Technical University of Athens,
Department of Applied Mathematics and Physical Sciences and ARVIUS S.A (CEO & Co-Founder)
c Independent Expert in Financial Markets and ARVIUS S.A (President & Co-Founder)
2013
1
Abstract
This work presents the results of an empirical research with the target of modeling the stylized
facts of the daily ex-post System Marginal Price (SMP) of the Greek wholesale electricity
market, using data from January 2004 to December of 2011. SMP is considered here as the
footprint of an underline stochastic and nonlinear process that bears all the information
reflecting not only the effects of changes in endogenous or fundamental factors of the market
but also the impacts of a series of regulatory reforms that have continuously changed the
market’s microstructure. To capture the dynamics of the conditional mean and volatility of
SMP that generate the stylized facts (mean-reversion, price spikes, fat - tails price distribution
etc), a number of ARMAX/GARCH models have been estimated using as regressors an extensive
set of fundamental factors in the Greek electricity market, as well as dummy variables that
mimic the history of Regulator’s interventions. The findings show that changes in the
microstructure of the market caused by the reforms have strongly affected the dynamic
evolution of SMP and that the best found model captures adequately the stylized facts of the
series that other electricity and financial markets share. The dynamics of the conditional
volatility generated by the model can be extremely useful in the efforts that are under way
towards market restructuring so the Greek market to be more compatible with the
requirements of the European Target Model.
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1. Introduction
Liberalization and deregulation of Electricity Markets, two facts that have characterize, in the
last decades, this industry, are the main drivers, behind a gradual increase of the degree of
structural complexity. Therefore, the decision making process of the market’s agents
(generators, distributors, suppliers, system operators, regulators etc.) is extremely difficult due
to uncertainty, nonlinearity and unpredictability that are inherent characteristics of any high
dimensional and nonlinear complex structure. The most representative feature of the
complexity of electricity markets is its price volatility and the associated with it stylized facts
i.e the nature of its statistical properties. Volatility is roughly the continuous change with time
of the standard deviation of price changes, conditional on the most recent information
available, a concept that is central in this paper. Electricity price volatility has a set of peculiar
“footprints” (the aforementioned stylized facts), which are universal statistical characteristics
commonly encountered in financial markets (Campbell J., et al, 1997, Taylor J.S., 2005).
There will be cases in which demand exceed supply (e.g when Unit availability is constrained or
equivalently load is curtailed) and competitive pricing is impossible, causing prices to exhibit
high volatility i.e. price spikes the level and duration of which are difficult to forecast (an
ideal condition for the exercise of market power). Inadequacies also of the Transmission
system enhance the complexity of Electricity markets which become more prone to problems
with local market power
The Greek Electricity Market, GEM henceforth, as all other Day-Ahead markets, exhibits a high
degree of volatility. This is because both demand-side and supply-side of the market depend on
a large number of fundamental variables i.e. the phase space of the dynamics of the market is
high dimensional and very complex. Price of fuel and CO2, Hydropower reserves, Power Plant
Unit availability, Renewable Energy Station (RES) power generation, are some of the supply
variables while labor factors, other macroeconomic variables as well as temperature constitute
the set of demand factors. Another factor that has increase the degree of complexity (and so the
price volatility) of GEM is the gradual and dramatic increase of the number of its agents
(generators, suppliers, marketers or qualified energy brokers and of licensed companies that
trade electricity), during the last five years. As a consequence of this high volatility is the need
for the adoption in the market of a number of hedging instruments used in financial markets to
reduce the degree of uncertainty, inherent in volatile markets. This is also a requirement of the
Target Model described below.
Greek Electricity Market, is a component of the Central – South European regional market (CSE
Region), together with France, Italy, Germany, Austria, and Slovenia, heading towards its
coupling, in the end of 2014, with the Unified European Electricity Market or Target Model1
which is in a process of developing. To this target, RAE, the Regulator of the market, proposes
its drastic restructuring in order to alleviate all possible current distortions and simultaneously
to enhance the degree of competition within the market as well as its structural compatibility
requirements of the target model. The most pronounced structural incompatibilities are: a)
GEM’s indirect auctioning system of short-term interconnection rights b) the lack of intra-day
market component c) market’s operation schedules not coordinated with other markets d) the
co-optimization of Energy and Ancillary services e) its DAS technical solution f) Market’s
clearance issues g) regulated max/min Bidding prices h) variable cost recovery mechanism and
j) its incompatible structure to adopt a forward market, FM.
The introduction of FM is by itself one of the structural changes in the market that has to be
made so GEM can be well “fitted” to the Target Model. Forward Contracts are expected to be
introduced in the GEM for example in the form of Generation Bids auctioning, written in such a
The principles of designing this new European Electricity Marker are described in details in the site of ACER
(Agency for the Cooperation of Energy Regulators).
1
3
way to account for different zones of Consumption and having different maturity time as well
as contracts related to Financial or Physical Transmission Rights (RAE 2011).
However, any efforts towards alleviating the distortions of the market, restructuring –
reengineering the market to meet Target’s model standards, have as a prerequisite an, in depth,
understanding (qualitatively as well quantitatively) the underlying dynamics of the wholesale
or system marginal price, SMP, as this key variable is the criterion for assessing the overall
efficiency and effectiveness of the market. By adequately modeling the stylized facts, i.e. the
dynamic evolution of SMP one can extract valuable information on the functioning of the
market since the effects of any distortions and inefficiencies are “incorporated” in the dynamics
of SMP. This in depth understanding of current and future dynamic evolution of the SMP can be
achieved, by using models that are capable of replicating the underlying dynamics of SMP on
which the pricing, in the near future, of forward Contracts will be based.
We provide at this point a short list of papers on stylized facts. Cont (Cont R., 2001) argues that
a complete as well as representative list of stylized statistical properties of financial asset
returns is as follows: Absence of autocorrelations, Gain/loss asymmetry, Heavy tails,
Aggregation Gaussianity, Intermittency, Volatility clustering, Conditional heavy tails,
Slow decay of autocorrelation in absolute returns, Leverage effect, Volume/volatility
correlation and finally, asymmetry in time scales. Weron (Weron R., 2006) provides for
electricity prices returns, a similar list of stylized facts that indirectly incorporates all the above,
as follows: Price Spikes, Seasonality, mean-reversion and Heavy tails in the distribution of price
returns. In the work of C. Dipeng and D. Bunn (Dipeng C. and D. Bunn, 2010) the stylized facts of
mean-reverting and spiky characteristics of spot prices are captured by a regime-switching
model and they are considered to be as the nonlinear effects of some exogenous factors acting
on spot prices. Exogenous factors as demand, reserve margin, large fuel price changes, Carbon
emission allowances and market concentration-power have nonlinear effects on spot prices
and consequently on their stylized facts. Regime-switching models are also used by Deng
(1998), Huisman and Mahieu (2003), Ethier and Mount (1999), to capture price spikes.
Huisman (Huisman R., 2009) provides an extensive review of the characteristics or stylized
facts of electricity prices. In their recent work Huisman and Kilic (Huisman R. and M. Kilic,
2011) examine the evolution of seasonality, mean reversion, time-varying volatility and price
spikes in the day-ahead electricity prices for the Belgian, Dutch, German, French and
Scandinavian markets over the years 2003-2010. The impact of changes in the level of reserve
margin on price spike is examined by Mount (Mount T. et al, 2006), by employing a regimeswitching model. It is shown that the probability of a spike increases in periods with low
reserve margins. Stylized facts of the Spanish daily spot electricity prices and especially the
leverage effect characteristic is examined (see section 7 in this work), by using a threshold
asymmetric autoregressive stochastic volatility (TA-ARSV) model, are described in the work of
Montero et. al (Montero J.M. et al, 2010). Huisman (Huisman R., 2008) employed switchingregimes models and found that the probability of price spike occurrence increases when
temperature deviates substantially from its mean level. Schwartz (Schwartz E.S., 1997) has
shown that commodity prices, exhibit strong mean reversion. Pilipovic (Pilipovic D., 1997),
Weron (Weron R., and B. Przybylowicz, 2000) and Simonsen (Simonsen I., 2003) also have
observed that electricity spot prices exhibit strong mean reversion as well. If jump behavior is
included in the models, the accuracy in capturing the stylized facts is increased as it has been
shown by Kaminsky (1997), Barz and Johnson (1998), Deng (1998), (Deng et al., 2001) and
Kamat and Oren ( 2001). Long range correlations, measured by Hurst exponent, are examined
by Erzgraber (2008). Volatility clustering in electricity markets and its comparison with the
one exhibited by financial markets is described by Weron (Weron R., 2000), and Perello
(Perello J. et al, 2007). Very high volatility expressed as a large number of very large or
extreme changes in price values is investigated by Bystrom (Bystrom H., 2005), for Nord Pool,
using extreme value theory. We refer also the works by Serletis and Rosenberg (Serletis A.
and A.A. Rosenberg, 2009, 2007) Elder and Serletis (Elder J. and A. Serletis, 2008) and finally
Kyrtsou et.al, (Kyrtsou C. et. al, 2009) in which evidence is provided for long memory of
4
antipersistence form (detected by Hurst exponents or detrending moving average, DMA). The
quantification of complex multiscale correlated behavior and the role of neglected
nonlinearities in electricity markets and in energy futures prices (as opposed to spot prices)
are also examined in these works, contributing further to the attempts to describe the degree of
complexity of energy markets in general compared to the one of financial markets.
To our knowledge, this is the second empirical work addressing the impact on GEM’s System
Marginal Price of Regulatory Market Reports or Policy changes (the first attempt is the work of
Kalantzis (Kalantzis K. et. al, 2012). However the main advantage of this work however is the
use of an extensive number of fundamental factors of the Supply side of the market, as
exogenous regression variables and the in depth analysis of the combined interactions of these
quantitative variables with the qualitative or dummy variables representing the regulatory
reforms and their effects on SMP. Previous similar works are those of Boffa (Boffa et. al, 2010),
Bollino (Bollino et. al, 2008 a,b ) and Bosco (Bosco et.al, 2007). This paper enhances the
relatively poor literature on modeling GEM’s dynamics (the work of Theodorou P., et al, 2008 is
dealing with SMP dynamics but does not consider regulatory impacts). This issue is also related
to the recent work of Bask and Widerberg (Bask M. et al, 2009) in which the interaction
between market structure and stability and volatility of spot prices is examined. However, the
work conceptually closer to ours, both on its general scope as well as on its specific research
questions on how regulatory reforms and polices in the Italian market impact the dynamics of
SMP, is the work of Petrella (Petrella et. al, 2012).
The main objective of this work is to answer the following questions: to what extent do typical
characteristics or stylized facts of electricity spot prices encountered in other markets do exist
in the Greek electricity market? Is there any inter-dependence between the gradual formation
of the structure of the Greek electricity market (through its regulatory reforms that the market
has undergone) and the dynamics of its SMP volatility, stability or complexity? How this
interdependence can be detected via quantifying the associated stylized facts? How different
are the stylized facts of an emerging electricity market as the Greek one, compared to other
fully-developed markets as e.g. the neighbor more mature Italian market or the Nord Pool?
Another goal is also to contribute to the growing literature on individual case studies and
comparisons of different electricity market architectures and their associated stylized facts of
prices, worldwide (Escribano et al., 2002, Andrianesis et al., 2011).
Therefore the authors believe that the findings in this work could be useful as follows:
a) To help in shedding light on any distortions – malfunctions and structural frictions that
exist in GEM and more importantly in revealing and quantifying the effects of the
Regulatory changes (by searching for example the side – effects of introducing, such
mechanism as the Transitional Capacity Adequacy and Cost Recovery mechanisms),
therefore contributing to the efforts of the appropriate markets’ agents (Regulator,
System Operator etc.) to detect those structural elements that have to be changed.
b) Indirectly, by using the findings in this paper to contribute to the efforts of restructuring and re-engineering GEM, via a better understanding of the dynamic
behavior of SMP, an information needed in the process of developing the forward
market.
The rest of this paper is organized as follows. In section2 we briefly describe GEM, the time
history of its architecture and the regulatory market reforms with the expected effects on SMP.
Section 3 provides complete description of the data sets, their pre-processing and required
tests before modelling. In section 4 we give the specification and fitting results of a number of
models, the best model found and the necessary tests on its innovations to assess how
successful the model is in replicating the stylized facts exhibited by SMP. In section 5 the
interpretation of results is presented while in section 7, using the model, we perform in sample
forecasts to replicate the impact of reforms on SMP and also compare GEM characteristics with
5
those of other electricity and financial markets. The paper concludes with conclusions and
propositions for further research.
2. Greek Electricity Market (GEM)
Greece has adopted in 2005 a pure mandatory pool for the wholesale electricity market. Its
implementation was carried out in stages or transitional phases (2000 – 2005, 2005 – 2010 and
2010–today). The revised market architecture, launched in September 2010, completed in
2011 its first full year of application, has determined the Day-Ahead (DA)2 SMP as the
wholesale market index reminiscent to S&P or ASE index, as this price determines in great
amounts the cash-flows of market’s players. This market design encapsulate fully the all the
requirement of the Grid and Market Operation Code of 2005. The design makes a clead
distinction between the DA market and Balancing mechanism. The evolution of Index HHI3
which measures the degree of openness of a market to competition has been reduced from the
value of 10000 in years 2008 and 2009 to 6844 in 2010 and 5764 in 2011, an improvement of
the market evolving to a more competitive state. However, GEM is far from being considered a
competitive market.
2.1 A brief description of GEM’s architecture and microstructure
Table 2.1 summarizes the time evolution of the net generation capacity for Greece. We observe
a gradual decrease in the share of Lignite Units in the total mixture and an opposite behavior in
the share of Natural Gas units due to constantly increasing number of investments of
Independent Power Producers (IPPs). More specifically, CCGT Units during period 2004 – 2011
have increased their share about 124%. The market was completely dominated by PPC until
2004. Table 2.2 provides a comparative view of the fuel-Mix generation 2010-11 in the
Interconnected system of GEM. Table 2.3 provides information on the market volume as well as
peak power demand for the period 2005-2009. Market volume is defined as the traded volume
of electricity and is equal to the annual demand (including the interconnection balance), i.e. to
52,365.8 MWh in 2010 and 51,872.3 in 2011. There are not yet any futures and OTC markets.
The Greek Electricity System consists of 13 Hydroelectric Stations, HES, installed in six river
systems. For example, see Table 2.4, the Aheloos river system has three hydraulically coupled
HES, Kremasta, Kastraki and Stratos. The total energy reserves of the three HES’s dams is the
times series of the regressor Ahelenr in table 2.3. The treatment of coupled HES gives a unified
water value which can be interpreted as opportunity costs of using reservoir water at a specific
time and not at an optimal later point of time. The HES production depends on the water
flowing out of the Dam and water management must be done in such a way that the dam levels
must remain within required range. If the water reserves in a Dam are high, HES Units must
operate in order to avoid waste of energy due to overspills, while in case of low water reserves,
operations must be constrained.
Among the Hydro variables the HES of the Aheloos river has the greater influence, followed by
the impact of HES of the Aliakmon river (see correlations -0.58 and -0.37 respectively of SMP
and energy reserves variables). For the period of October 15 to end of May each year, water is
collected in the Dams while Hydro generator is practically zero. From beginning of June to midOctober Hydro must-run (for irrigation etc) and generation is taking place. Strong correlations
2
A short description of the Day-Ahead (DA) market is given in Appendix 1.
HHI stands for Herfindahl-Hishman Index. If HHI = 10000 the market is a monopoly, if HHI > 5000 the market is
over-concentrated, H > 1800 concentrated,
for 1000 < HHI < 1800 efficiently competitive and HHI ≤ 1000
competitive.
3
6
are observed, as expected, between Kremasta Hydro-Dam level (in meters) and the
corresponding Aheloos energy reserves (MWh) (0.98), and Polyfito Dam level and Aliakmon
energy reserves (0.97).
Table 2.1: Installed capacity as of 2004, and 2007 - 2011 in the interconnected system
Plant Type
Lignite
31.12.2004
Net
installed
%
capacity
(MW)
31.12.2007
Net
installed
%
capacity
(MW)
31.12.2008
Net
installed
%
capacity
(MW)
31.12.2009
Net
installed
%
capacity
(MW)
31.12.2010
Net
installed
%
capacity
(MW)
31.12.2011
Net
installed
%
capacity
(MW)
4,808.00
43.92%
4,808.00
40.50%
4,808.10
38.69%
4,808.10
38.49%
4,746.00
33.74%
4,496.00
31.30%
718.00
6.56%
718.00
6.05%
718.00
5.78%
718.00
5.75%
698.00
4.96%
698.00
4.86%
1,572.00
14.36%
1,962.00
16.53%
1,962.10
15.79%
1,962.10
15.71%
3,224.00
22.92%
3,526.00
24.55%
487.00
4.45%
487.00
4.10%
486.80
3.92%
486.80
3.90%
487.00
3.46%
487.00
3.39%
3,017.00
27.56%
3,017.00
25.41%
3,016.50
24.27%
3,016.50
24.15%
3,018.00
21.46%
3,017.00
21.00%
345.00
3.15%
880.00
7.41%
993.50
7.99%
1,058.40
8.47%
1,558.00
11.08%
2,141.00
14.90%
Large-scale
CHP
334.00
2.69%
334.00
2.67%
334.00
2.37%
Other
Cogeneration
108.00
0.87%
108.00
0.86%
HFO (Heavy
Fuel Oil)
CCGT (Gas
Turb. Combin.
Cycle)
Natural gas –
other (Gas)
(OCGT)
Hydro plants
(large)
RES and small
Cogeneration
Total
10,947.00 100.00%
11,872.00 100.00%
12,427.00 100.00%
12,491.90 100.00%
14,065.00 100.00%
14,365.00 100.00%
Table 2.2: Fuel-Mix Generation 2010-11 in the Greek Interconnected System
2010 (ΤWh)
2011 (ΤWh)
% difference
Lignite
27.44
27.57
0.47
Fuel Oil
0.11
0.009
-91.82
Natural Gas
10.36
14.85
43.34
Large Hydro
6.70
3.68
-45.07
RES
2.04
2.53
24.02
Total Local Generation
46.6
48.6
4.29
Net Imports
5.70
3.23
-43.33
Grand Total
52.35
51.87
-0.92
Source: ADMIE S.A.
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Table 2.3: Market Volume, i.e. Energy and peak power demand (2005-2011) for the
interconnected system (Source: IPTO - ADMIE)
Electricity
consumption
excluding
pump storage
(GWh)
2005
2006
2007
2008
2009
2010
2011
52,500.8
53,656.8
55,253.4
55,675.3
52,436.5
52,365.8
51,872.3
10,393
9,828
9,902
10,055
10,610
Peak load
(MW)
9,635
9,962
(11,110
including
curtailed
load)
Figure 2.1 provides information on the main structural components of the Greek wholesale
Electricity Market (taken from RAE’s 2010 National Report to the European Commission) (RAE,
2009 and 2010).
The wholesale electricity market under the Grid and Market Operation Code
Day Ahead
On the Day
After the Day
Imbalance
payments and
charges. Payments
for reserves and
ancillary services
provided
Producers
Energy and Reserve
Offers, Techno-Economic
Declarations, NonAvailability Declarations
Importers
Hydro and Renewables
Payments
Security constrained
Day Ahead Schedule
SMP
Q
System Marginal Price
(single for Suppliers, may
be zonal for Generators)
Primary and Secondary
Reserve Prices
Energy and
reserves
schedule,
satisfying
System and
Generating Units
constraints
Real Time
dispatch
Dispatch
Instructions
and
Adjustments
of Day
Ahead
Schedule
Charges
Suppliers
Exporters
Pumping Units
Dispatch
instructions
and
Instructed
Deviations
Calculation of
imbalances between
Measured and
Scheduled Production
(not included
Deviation).
Settlement at the
Imbalances Marginal
Additional Payments
for instructed
deviations
Transmission
System constraints,
Reserves needs,
Market Split rules
Declarations of
Load and Exports
(may be priced)
LAGIE (IMO)
Measurement
Data
DAS Settlement
of Accounts for
Energy
P
Imbalances
Settlement
Imbalance payments
and charges. Charges
for reserves and
ancillary services
provided
ADMIE (IPTO)
Figure 2.1.: Structural components of the Greek wholesale Electricity Market (taken from
RAE’s 2010 National Report to the European Commission)4.
4
Amended by the authors to depict the formation of two new entities i.e. LAGIE and ADMIE, out of the former HTSO
8
Table 2.4: Hydroelectric Stations and River systems in GEM
Hydro Electric Station Dam
Kremasta
Kastraki
Stratos
Polyfito
Sfikia
Asomata
Aoos Springs
Pournari I
Pournari II
Thisavros
Platanovrisi
Ladonas
Plastiras
River
Aheloos
Aliakmon
Araxthos
Nestos
Ladon
Tavropos
Total Installed
Capacity (MW)
437
320
150
375
315
108
210
300
34
384
116
70
130
2.2 Regulatory Market Reforms RMRs
Because one of the main targets of this work is the detection of the impacts of the various
reforms made, until today, by the Regulator on the SMP, we consider necessary a small
description of these reforms as this will help a lot in understanding the usefulness of the
modeling results of this work. The reforms took place on specific dates -milestones or
Reference Dates, within the aforementioned transitional phases. Regulator’s National reports
to EU (RAE, 2009,2010,2011) as well as other texts of the ADMIE and the work of Kalantzis
et.al. mentioned above, are the main sources of this brief description.
However, in all the previously referred official reports of the regulator regarding the prevailing
market conditions, it is a spread evidence that GEM exhibits significant structural distortions
and weaknesses that influence negatively its efficiency. These frictions are responsible for the
lack of real competitiveness in the market. As an example, Regulator has repeatedly pointed out
in reports the need for measures to constraint the excessive market power of the dominant
player in the market, PPC. The regulator considers that PPC behaves completely differently
than the other rivals due to the fact that it has a unique energy mixture,(consisting of Lignite
and Hydropower Stations that the other do not allow to have. This according to the regulator
and other players creates an asymmetry in the market and subsequently frictions impairing
efficiency.
More specifically, some of the measures taken by RAE towards avoiding abuses by PPC, are the
transparency of information, Techno-economic declarations of generation units, periodical
Hydro Usage declarations, Unit Availability declarations, Price Caps and Price floors (RAE,
2010). Given the fact that in general and in particular in GEM Hydro Generation has a crucial
impact on the formation of SMP, RAE requested PPC to publish 12-month rolling estimates of
mandatory hydro, reservoir inflows and storage levels and historical annual curves. Through
this measure, RAE’s purpose is to make possible deviations, between target and actual levels in
inflows and storage, more clear and amenable to potential corrections. A measure that also
gives to the traders the ability to adjust their positions in response to the published hydro
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schedules is the obligation of PPC to publish those schedules prior to the closure of the auctions
for interconnection.
1st Reference Day (1.10.2005) (RMR1). The 1st Reference Day (01.10.2005) marked the
beginning of a market-based operation of the system, with the System Operator dispatching
units according to an offer based unit commitment and the SMP calculation to be based on
offers instead of costs.A price floor was set (it is still in place) to the offers, corresponding to
each Unit´s minimum variable cost, in an effort to prevent the incumbent (dominant player
generating) from bidding below this value. This reform in combination with the entrance in the
market of a new IPP (ENTHES), was expected to have a positive effect (increase) on the
evolution of SMP. To facilitate the dispatching of Units, based on at least their technical
minimum, the price floor was not applied to the first 30% of the offered quality (rule of 30%).
2nd Reference Day (1.1.2006) (RMR2). The Capacity Adequacy Mechanism, CAM, aiming to
the partial recovery of capital costs, forces Suppliers to buy capacity certificates from
generators. In November 2010, until now, the value was set to 45000€/MWh/year, in an effort
to mediate the effect of low demand on the revenues of generators. CAM has created incentives
for new investments, inducing as almost 2000 MW of new IPP gas-fired capacity to be added to
the system by the end of 2011.CAM, has an effect on SMP depending on the degree of maturity
of the market (Stoft S., 2002) If the market is mature this mechanism is expected to have no
effect on the dynamics of SMP. The third Regulatory Market Reform, RMR3, was a result
caused by an almost continuous pressure by market agents to change the methodology of
estimating SMP. In addition to this, there were also expressed complaints by market players for
the operations of the System Operator regarding the dispatching of a number of Units, at all
times, for security reasons, some of them functioning at their technical minimum. A new
methodology was adopted aiming in changing the artificially low SMP determined due to the
above mentioned reasons, causing the agents to complaint, in which technical minimum were
not considered, therefore approaching to a pure economic dispatch. An increase in SMP was
expected due to this reform. RMR4 regards the change from daily to hourly submission of
generator offers, starting on 4th April 2007. According to this reform each generator could
submit for each trading day and for each hour, a different bid of higher value for peak hours and
low for off-peak ones. The SMP was expected not to be affected by this reform.
3rd Reference Day (1.5.2008) (RMR5). Cost Recovery Mechanism, CRM5, was considered
by the Regulator a necessary step until the Imbalance Settlement Mechanism, ISM
(scheduled for the 5th Reference Day). CRM states that if the SMP is lower than the marginal
cost of generating Unit (plus 10%), then the Unit will receive the difference as a compensation.
The Regulator expected that this Reform would have no effect on SMP. CRM was aiming to
ensure that generators will be compensated at least their marginal cost, in case they were
ordered to operate.
4th Reference Day (1.1.2009) (RMR6). The 4th Reference Day (01.01.2009) focused on the
change of the ex-post SMP calculation methodology according to the unit commitment
algorithm that considers all technical constraints of the units and the reserve requirements of
the ADMIE (ex HTSO) expecting to lead to lower SMPs.
5th Reference Day (30.9.2010) (RMR7). The 5th Reference Day (30.09.2010) initiated the
mandatory day-ahead market model and introduced the Imbalances Settlement Mechanism
5
This mechanism, currently in use, provides an explicit compensation for the commitment costs incurred as a
result of the market situation (generation scheduling) as well as additional payments so the Unit ends up with
a profit equal to 10% of its variable cost, if the market revenues for energy (taking into account both DA and
IS markets) is not capable of generating a reasonable profit (see also Andrianesis P., et.al , 2011).
10
retaining at the same time the SMP methodology allowing only the submission of demand
declarations. RMR7 is referred to the adoption of an enhanced Unit commitment algorithm
which co-optimize energy as well as ancillary services. In this new mandatory, Day-Ahead
market model incorporating, at the same time, an Imbalance settlement mechanism6, market
clearance is now based on the non- priced demand declarations (previously the HTSO forecasts
were used instead). Taking into account that the methodology for estimating SMP retained the
same and the fact that usually the declared demands were underestimated, the effect of this
reform expected to reduce SMP slightly. RMR8 regards the decision of the Ministry of Finance
(1.9.2011) to impose a new tax levy on natural gas, equal to 1.50€/GJ (applied also to electricity
generation). As SMP was set, for the majority of trading periods, by Natural Gas fired Units, the
resulted increased generation cost was expected to increase SMP (see section 6.1 for
comments). At the final stage the “architecture” of the market consists of the following
components: A Day-Ahead (DA) compulsory market, the Imbalances Settlement
Mechanism, the Capacity Adequacy Mechanism, the Cost Recovery Mechanism and the
Ancillary Services Market. GEM is supervised by the Regulatory Authority for Energy (RAE)
and is operated by the newly formed organizations, the Independent Power Transmission
Operator (IPTO or ADMIE) and the Independent Market Operator (IMO or LAGIE). We provide
a small description of these two bodies and a history of their formation process in the appendix
2. Table 2.5 summarizes all the Regulatory Market Reforms taken towards a resolution of the
distortions. In this table we provide the values of SMP and Load at the time of enactment of
each reform, in order to monitor the evolution of SMP returns and their volatility, after the
enactment. The last two columns give RAE’s expectations of the impacts these reforms may
have on SMP and the actual, observed in practice impacts that also happened to be reassured
by the modeling results of this paper. As we will see in a later section, for example, the Cost
Recovery mechanism had actually a positive impact on the evolution of SMP, as it is shown in
the last colum of Table 2.3, instead of an expected by the regulator neutral or uncertain one.
All imbalances – referring to the differences between the DAS (Day-Ahead-Schedule) and the real production or
withdrawal of electricity – are settled through the Imbalance Settlement Mechanism.
6
11
Table 2.5: History of Regulatory Market Reforms (RMR)
Regulatory
Market
Reform
(RMR)
Values at time of
Regulatory change
SMP
Load
€/MWh
MW
Regulator’s
expected
Impact of
RMR on SMP)
Actual
impact of
the
Reform
5322
upward
upward
27.46
4975
neutral
neutral
1st Change of methodology for
SMP calculation
41.04
6839
upward
upward
01.04.2007
Introduction of Hourly Bids
41.98
5292
neutral
RMR5
01.05.2008
Cost Recovery Mechanism
42.02
4544
neutral
upward
RMR6
01.01.2009
2nd Change of Methodology for
SMP calculation
47.97
5538
downward
downward
RMR7
30.09.2010
DA market (mandatory) with
imbalance settlement
52.79
5532
downward
upward
RMR8
01.09.2011
Introduction of Natural Gas
Consumption Tax
90.75
6509
upward
upward
Launching
Date of RMR
Description of the Regulatory
Market Reform
RMR1
01.10.2005
Adoption of mandatory pool (expost settlement)
63.12
RMR2
01.01.2006
Capacity Adequacy Mechanism
RMR3
13.01.2006
RMR4
downward
3. Data Sets, Processing and Tests
We have selected and analyzed daily data (average of 24 hourly data) on spot, Ex-post System wide Marginal prices, SMP, and load (demand) of the Greek Electricity Market, taken from the
official site of the Greek Independent Power Transmission Owner, IPTO, ADMIE S.A
(www.admie.gr). The data set cover the period from 01.01.2004 to 31.12.2011, i.e. it contains
2922 data corresponding to eight years. The market was less mature further back. Due to
transformations needed for some variable (e.g Brent Oil data), the final length of the data set
used in all calculations is 2877. We note that the SMP data for the period 01.01.2004 to
30.09.2010 are ex-post adjusted values while from 01.10.2010 to 31.12.2011 are ex-ante.
Figure 3.1 shows the evolution dynamics of SMP values. An upward trend which drives the
series is evident, causing an increase of X% in the period 2004-11. Regular (weekly, quarterly)
patterns can be seen, as well as some short-lived spikes and volatility clusters (although not
easily distinguished). We clarify, at this point, the characteristics of the chosen series for
analysis and modeling.
During the transitory market regime (2004 – Sept. 2010), an indicative plant – commitment
schedule was formed by the Day – Ahead market which also determine a SMP forecast as a
reference spot price, working mainly as a price signal. However, the Cash – flows were based on
Ex–post SMP prices which were the output of solving again the same cost – minimization
12
problem as in the case of Day – Ahead Schedule (DAS). This was possible by considering, in the
solution process, the actual metered values of inputs as demand (load), plant availabilities, RES
generation etc, and not DA forecasts. Then, Ex–post SMP prices were applied to the actual
generation (reflecting largely the real – time dispatch orders of the TSO) and Consumption
Volumes. Therefore, in the transitional period of GEM, Ex–post SMP used to settle the whole
market. After the RMR7 (30.09.2010), the new market design consists of two separate
settlement processes: the DA market settlement (in which generators are paid and suppliers
are charged according to volumes based on SMP and the plant schedules formed from DA
dispatch i.e. from load declarations submitted, and the Settlement of Imbalances. In this
settlement, deviations from DAS are charged or compensated (exogenous or TSO dispatch
orders). In DA market a uniform pricing is still in place, which reflects the offer of the most
expensive Unit dispatched, taking into Consideration the forecasted demand, plant technical
constraints and the needs for reserve capacity. Table 2.1a gives the summary statistics of the
Table 3.1a: Summary statistics of SMP_das and SMP_expost
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
DAS
56.35368
54.80146
117.9084
20.57900
18.05566
0.442226
2.804380
EXPOST
61.55577
59.81215
150.0000
20.37208
19.24139
0.655339
3.824370
Jarque-Bera
Probability
87.38570
0.000000
255.3301
0.000000
Sum
Sum Sq. Dev.
144040.0
832947.1
157336.5
945940.1
Observations
2556
2556
160
140
120
Euro/Mwh
100
80
60
40
20
0
2005
2006
2007
2008
DAS
2009
2010
2011
ExP
13
Figure 3.1a Time histories of SMP Das and SMP ex-post, 2004-11.
160
140
Euro/Mwh
120
100
80
60
40
20
0
DAS
ExP
Fig. 3.1b Box plot of SMP Das and Ex-post .
two prices . Figures 3.1a ,b show the co-evolution dynamics and the distribution comparison.
In the box plot, the values of the SMP ex-post distribution parameters (3rd quartile, mean,
median and 1st quartile) are slightly higher than those of SMP-das. However the number of
extreme or outlier values is larger and more extensively distributed in the case of SMP ex-post.
As temperature is probably the most commonly used load predictor which in turn influences
heavily SMP we examine the (linear) correlation coefficient between load and minimum,
maximum temperature data from meteorological stations installed by NTUA, National
Technical University of Athens. Table 2.1b shows daily max and min temperatures in
Thessaloniki (the second largest city of Greece, in North) and in Athens (South). We observe
that until 2009, North and South , load is correlated with min and max temperature almost the
same. However, during the last two years 2010-2011, the correlation becomes more intense,
both in two regions, while in 2011 in Athens we observe a greater correlation of load with min
temperature indicating a more intense usage of AC for heating during winter due to a more
expensive price of heating Oil and Nat Gas (a tax was imposed by the Government). The
variation of Load with the daily average temperature in the country is shown in figure 3.2.
Table 3.1b Correlation coefficient between daily average Load and Temperature
Time Period
Full series
2007
Correlation coefficient between daily average Load and Temperature
THESSALONIKI
ATHENS
o
o
o
min temp. C
max temp. C
min temp. C
max temp. oC
0.29
0.29
0.35
0.32
0.16
0.15
0.17
0.16
14
2008
2009
2010
2011
0.14
0.14
0.43
0.42
0.11
0.17
0.44
0.43
0.21
0.19
0.48
0.48
0.18
0.19
0.48
0.44
10000
9000
y = 8.2*x 2 - 2.6e+002*x + 7.6e+003
Load MWh
8000
7000
6000
5000
load vs AvgTemperature
4000
quadratic
3000
-5
0
5
10
15
20
25
Daily Average Temperature (Deg. Celcius)
30
35
Figure 3.2 Load variation with average daily temperature in Greece. In the quadratic equation
shown x is temperature and y Load.
The graph shows a parabolic shape indicating increased consumption at high and low
temperatures. It suggests also that forecasting future load (demand) requires the knowledge of
load growth profile, relative to a certain reference i.e the current year. The polynomial function
of load versus temperature shown on the graph seems a reasonable approximation for load
forecasting. Due to quadratic and strong correlation between temperature and load, we have
not included temperature as an exogenous – regressing variable in the modeling since its effect
on SMP is sufficiently captured by the load variable.
The data for Imports and Exports of Energy (in MWh) were taken from interconnection
measurements (per interconnection point). The Generation Thermal Units availability data are
daily final while for the availability of Hydro Units we considered their contractual values.
The management of some missing values in the SMP spot price vector was done by using a
combination of approaches like average of the neighboring observation for sporadic missing
values. An overview of the data is given in Table 3.2.
15
Table 3.2: List of data set and name of Variable used in Modeling.
Name of Data TS
1
SMP ex-post or
SMP
2
Load
3
Brent
4
HydMR
5
HydGen
6
Ahelenr
7
Aliakenr
8
Araxthenr
8
Ladonenr
10
Nestosenr
11
Plastenr
12
Hfog
13
Resgen
14
Ligng
15
Natgasg
16
TotImports
17
TotExports
18
Uvail
19
MinTempNTUA
MaxTempNTUA
AvgTempNTUA
Description
Length
of Time
Series
Resolution
Units of
Measure
Daily
€/MWh

Monthl
y
Source
Period
Covered

IPTO Data Base
2004-2011
IPTO Data Base
ICE (Inter.
Exchange,
Blooberg 20042012)
2004-2011
Ex-post System
Marginal Price
(GEM Pool)
Load or Demand
2877
2877
MW

Brent Crude OIL
Price
2877
$/pbl

See
note
2877
MWh


IPTO Data Base
2004-2011
2877
MWh


IPTO Data Base
2004-2011
2877
MWh


IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
MWh


IPTO Data Base
2004-2011
2877
MWh


IPTO Data Base
2004-2011
2877
MWh

IPTO Data Base
2004-2011
2877
oC

National
Technical
University of
Athens, NTUA
2004-2011
Hydro Production,
must-run
Hydro Production
Energy Reserves of
Aheloos Dam
Energy Reserves of
Aliakmon Dam
Energy Reserves of
Arahthos Dam
Energy Reserves of
Ladon Dam
Energy Reserves of
Nestos Dam
Energy Reserves of
Plastiras Dam
Heavy Fuel
Generation
Renewables
Generation
Lignite Generation
Natural Gas
Generation
Total Imports of
Energy
Total Exports of
Energy
Generating Unit
Availability
Min, Max,
MeanTemperature
in Athens

2004-2011
Figure 3.3 and 3.4 show the SMP (raw data) and load (demand) time histories. It is apparent in
fig. 3.3 that SMP exhibit a characteristic known as volatility clustering , that large changes and
small changes tend to have their own clusters. The concept of volatility clustering is further
explained in the sections that follow.
16
SMP (ex-post daily) Time Series 2004-2011 ( ADMIE data )
150
RMR8 01/09/2011
RMR5 01/05/2008
RMR4 01/04/2007
RMR2 01/01/2006
100
RMR3 13/01/2006
Euro/Mwh
RMR1 01/10/2005
50
RMR7 30/09/2010
RMR6 01/01/2009
0
2004
2005
2006
2007
2008
2009
2010
2011
2012
Time (Days)
Figure 3.3.: Time history of the ex-post System Marginal price, SMP, of the Greek Electricity
Market, 2004-2011. The arrows locate the dates of regulatory changes.
Daily, System-wide, Load 2004-2011 Greek electricity Market (IPTO data)
10000
9000
8000
Mwh
7000
6000
5000
4000
3000
2004
2005
2006
2007
2008
Days
2009
2010
2011
2012
Figure 3.4.: Time history of the daily, system-wide, load of the Greek electricity market 20042011.
17
Table 3.3: Summary statistics of SMP
Period
Min
Euro/Mwh
Max
Euro/Mwh
Mean
Euro/Mwh
Std Deviation
Euro/Mwh
Coefficient of
Variation
(a Volatility
proxy)
Skewness
Kurtosis
Inter
Quartile
Range
Euro/Mwh
2004
16.97
45.19
30.00
5.22
0.17
-0.1578
2.614
7.22
2005
20.37
80.16
43.13
11.97
0.28
0.5246
2.986
15.66
2006
26.91
81.19
64.13
12.06
0.19
-0.8428
3.5010
18.91
2007
33.82
84.97
64.94
9.27
0.14
-0.6681
3.3435
12.93
2008
30.92
124.35
87.23
14.23
0.16
-0.4520
3.999
19.12
2009
29.19
73.66
47.39
9.67
0.20
0.3630
2.7483
12.91
2010
29.42
83.12
52.25
10.51
0.20
0.1783
2.4992
15.07
2011
35.94
150
71.70
20.11
0.28
1.4048
5.800
23.07
2004-2011
16.97
150
57.00
20.36
0.36
0.540
3.464
30.25
Table 3.3 gives the descriptive statistics of daily SMP. The positive skewness and kurtosis of the
entire series indicate that the distribution of SMP has an asymmetric distribution with a longer
tail on the right side, fat right tail. SMP is clearly non-normally distributed, as it is indicated by
its skewness and excess kurtosis (>3) (normal distribution has kurtosis ≈3).
Table 3.4 provides summary statistics for SMP and log SMP (the choice of this transformation is
explained below) together with results from normality tests applied on the series, using the
Jarque – Bera, JB algorithm (Jarque C.M. and A.K. Bera, 1987) of the null hypothesis that the
sample SMP has a normal distribution. The test rejected the null hypothesis at the 1%
significance levels, as it is shown in the table (p=0.000, JB Stat significant). As it is shown in a
later section, SMP follows a distribution of fat tail, a student’s t distribution.
Table 2.4 Comparing summary statistics of SMP and log SMP
SMP
LOG(SMP)
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
56.98370
56.07000
150.0000
16.97000
20.36816
0.540037
3.464248
3.975591
4.026601
5.010635
2.831447
0.375986
-0.371518
2.650906
Jarque-Bera
Probability
165.6774
0.000000
80.79185
0.000000
Sum
Sum Sq. Dev.
163942.1
1193142.
11437.77
406.5675
2877
2877
Observations
18
In figures 3.3 the SMP exhibits also, besides volatility clustering, the typical features of mean
reversion and spikes, a tendency of the data to fluctuate around a long-term stable state or
equilibrium, as well as extremely high values of short duration (spikes). Figure 3.5 shows the
quantile-quantile plot of SMP against a theoretical normal distribution, In case the empirical
and assumed theoretical distributions are the same, the q-q plot should be a straight line. The
deviation of SMP from normality is apparent in the q-q plot. We see that the empirical quantiles
(blue curve) versus the quantiles of the normal distribution (red line) do not coincide, even
slightly, and exhibit extreme right and left tails: the maximum for SMP data is a multiple of 4.8
of the standard deviation, often far larger than the factor around 3.46 that the normal
distribution suggests. The extreme right tails of SMP will be used later as a way of describing
the spikes that are shown in the conditional volatility series. Summary statistics of all the
exogenous quantitative explanatory variables, used in modeling process is given in the
Appendix 3 of this paper.
QQ Plot of SMP ex-post (2004-2011) versus Standard Normal
(ADMIE S.A 2004-2011 data)
160
140
Quantiles of SMP ex-post
120
100
80
60
40
20
0
-20
-40
-4
-3
-2
-1
0
1
2
3
4
Standard Normal Quantiles
Fig. 3.5: Quantile – Quantile plot of ex-post SMP against the normal distribution
3.3 Testing for stationarity of the SMP returns
We treat SMP as a stochastic process and before proceeding to further in our analysis, it is
necessary to check the series for lack of stationary. Economic and Financial time series, due to
the fact that they depend on exogenous factors, exhibit a non-stationary behavior (Brock A.W.
and P.J.F. de Lima, 1995, Pagan A., 1996). However, it has been found that electricity market
data are more stationary than all financial series, reported so far in empirical analyses (Strozzi
F. et. al., 2002, Bunn 2004, Weron R., 2006). Augmented Dickey_Fuller (ADF) and PhillipsPerron (PP) unit roots tests have been performed, for testing the null hypothesis that SMP has
unit roots i.e is nonstationary. Table 2.5 lists the results.
19
Table 3.5 ADF and PP test for Normality.
Lag
0
1
2
3
4
5
6
7
h
1
1
1
1
1
1
1
1
p
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
ADF Stat
-12.9068
-10.4557
-8.6783
-7.6094
-6.8322
-5.9425
-5.0524
-5.6615
h
1
1
1
1
1
1
1
1
p
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
PP test
-12.9068
-11.9549
-11.2853
-10.9366
-10.7832
-10.6480
-10.5460
-10.8849
The logical flag h = 1 indicates a rejection of the null hypothesis (critical Value for both tests is 3.414 a value less than the Stats values above). Therefore SMP with high probability is
covariance-stationary around a linear trend. Theodorou (Theodorou P., et. al, 2008, Petrell et.
al, 2012) have reported similar with us results using Dickey – Fuller (DF) and Kwiatkowsk –
Phillips – Schmidt – Shin (KPSS) tests. Papaioannou G., et al. (1995) and Papaioannou G.,
(2013), have applied a nonlinear tool for stationarity detection in financial and electricity
markets.
ADF unit root tests reject the null hypothesis of the existence of this type of nonstationarity for
all Hydro Plants (energy reserves series) and the Brent oil one (ADF Stats > CriticalVal).
Therefore, for these series we take first differences to make them stationary. SMP and all
quantitative explanatory variables are not Normally distributed as the JB test suggests, so we
log transform them to make them ‘more normal’ (JB Stats are reduced and become
insignificant) (see Appendix 3 for test results).
3.4 Autocorrelation and Partial Autocorrelation functions
Autocorrelation estimates of SMP and its returns are presented in this section. They signal the
extent to which prices carry over from one day to the next. Arbitrage opportunities are
associated with non-zero autocorrelations.
In figure 3.6 we plot the ACF of the system marginal price for the period 2004-2011. We
observe strong, persistence 7-day dependence and that the ACF decays very slowly. This
indicates that SMP data contain a strong trend which is responsible for this positive and very
slowly decreasing ACF. Brownian motion, commodity prices etc. behave similarly, yielding very
slowly decaying ACF’s. However, these serial dependencies can be “destroyed” by taking
differences in the data which is equivalent of taking the returns of the data. Since we are
interested in revealing the impacts of exogenous variables (that exhibit both trend and
periodicity) on SMP and since SMP series was found to be stationary we do not take differences
of the series and let our proposed composite ARMAX/GARCH model to take care of these
dependencies.
We have also calculated ACF and PACF (not shown here) of SMP returns and square returns (a
proxy for variance) in which we see also that there is a strong, persistent of one-, two-, sevenand 14-day dependency in contrast to most financial data for which ACF of returns dies out
quickly to zero after the first lag or after 5-10 lags (e.g. days) and long-term autocorrelations
are observed only for squared returns (results are not included here due to space limitation).
While the existence of such large autocorrelations indicates lack of market efficiency, the
inherent characteristic of non-storability of electricity does not allow traders to take advantage
20
for profits from such day-to-day dependence. The one- and two-day autocorrelations are due to
the timing of bids. For example, bids for tomorrow delivery must be submitted today. So, the
information set available at the time tomorrow’s bids are submitted, includes yesterday’s
information but not today’s one, therefore a two-day lag autocorrelation. Also, electricity
demand varies from Sunday to Monday, and this variation is almost the same. The expected
day-of-the-week effects observed in all electricity markets explain the 7- and 14-day lags in the
ACF.
Autocorrelation of SMP expost 2004 2011
1
0.5
0
-0.5
0
5
10
15
Lag
20
25
30
25
30
Partial Autocorrelation of SMP expost 2004-2011
1
0.5
0
-0.5
0
5
10
15
Lag
20
Fig. 3.6 : Autocorrelation and Partial Autocorrelation function of SMP (2004-2011)
The results obtained in figure 3.6 are useful in model specification for the conditional mean. A
quantification of the correlation existence is possible by using a formal hypothesis test, the
Ljung-Box-Pierce Q-test for a departure from randomness based on the ACF and PACF on SMP.
It is known that the Q-test is most often used as a post-estimation lack-of-fit test applied to the
fitted innovations (residuals)(see below). We have applied the above test using seven lags
(weekly dependence) to test the null hypothesis of no serial correlation, under which the Q-test
statistics is asymptotically x2 distributed.
Table 3.6 Lung-Box-Pierce Q-test results on SMP
lag
1
2
3
4
5
6
7
ACF
0.907
0.854
0.828
0.809
0.797
0.795
0.802
PACF
0.907
0.183
0.168
0.118
0.099
0.134
0.152
Q-Stat
2366.9
4469.9
6443.5
8332.5
10162
11985
13843
prob
0.000
0.000
0.000
0.000
0.000
0.000
0.000
21
Based on the results, the null of zero serial correlation is rejected at the 99% significance level.
We have also implemented Engle’s test to test for the presence of ARCH effects. Under the null
hypothesis that a time series is a random sequence of Gaussian disturbances (i.e. no ARCH
effect exist), this test statistics is also asymptotically x2 distributed. This test too rejected the
null hypothesis that there are no significant GARCH effects (the results are not shown here). As
a conclusion, the SMP series exhibit both significant correlations and GARCH effect or
heteroskedasticity. This enhances our decision to apply a GARCH model for conditional
volatility and its associated stylized effects.
Therefore, we are sure with a high certainty that the SMP series is covariance-stationary
around a linear trend. Our result is in line with other previous works on electricity prices
(Petrella, et. al,2012, Bunn, 2004, Werron, 2006). However, since we have found that SMP is not
normally distributed we just take the log of the series to make it ‘more normal’ (actually the
Jarue-Bera statistics see table 2.4 is reduced from 165.7 to 80.7).
Thus, based on these results, our models for conditional mean and volatility will be specified in
log levels, that is we take log-transform and no differences. We expect that the linear trend
mentioned before, may be nothing but a proxy for the underline trend in a fundamental factor
as for example fuel prices. In fact, looking at the correlation table, between SMP and exogenous
variables in Appendix 4 and the following figure 3.7 showing the Price Index changes in 20022009, one can expect that the linear trend may come from Nat Gas prices (correlation
coefficient 0.57), Brent price (corr. Coef. 0.62) and load demand (corr. Coeff. 0.40). The
conditional mean equation described below will give as a more certain answer for the linear
trend, around which the SMP is covariance-stationary,
Price Index dynamics (Base : Jan 2009=100)
240
200
160
120
80
40
0
2002
2003
2004
2005
SMP
HEAVYFUEL
CO2
2006
2007
2008
2009
Nat Gas
Diesel Oil
Figure 3.7 Price Index dynamics of SMP and Fuels (source :FEIR report 20107)
7
Foundation for Economic & industrial Research (IOBE), report 2010.
22
4 Modeling conditional mean and Unconditional (Historic) and Conditional
Volatility of SMP
Historical or statistical volatility, HV, looks backward i.e. it is based on past return values,
unlike implied volatility which is a concept used in the option pricing theory, giving an
estimation for the future volatility. HV is simply the annualized standard deviation, St.dev, of
past or historical returns. HV or retrospective volatility index therefore captures the amplitude
of price movements for a given period of time in the past. All typical risk theoretical models that
rely on the notion of standard deviation generally assume that return conform to a normal bellshaped distribution. In that case, therefore, we can expect that about two-thirds of the time
(68,3%), asset returns should fall within one st.dev (+-) while 95% of the time they should fall
within two st.dev. Qualitatively normal distributions exhibit skinny “tails” and perfect
symmetry. Using the rolling volatility method we estimate a rolling standard deviation i.e. the
st.dev of returns measured over a subsample which moves forward through time, thus
estimating volatility at each point in time. It is assumed implicitly in this approach that
volatility is constant over the time interval corresponding to the chosen subsample. This
method provides accurate values of st.dev, when we are interested in point estimation, and
assumes also that returns follow a geometric Brownian motion (Merton, R., 1980).
However the assumption of constant volatility over some period is both statistically inefficient
and inconsistent, in estimating volatility. We handle this problem by building first parametric
models for the time-varying st.dev and then extract volatility from return data generated by the
model. The models described in section 10 below (of the GARCH-type) are used to give better
estimates of volatility of SMP.
The moving window approach or rolling volatility approach gives the volatility estimate at
a given time tk (Weron R., 2006, Eydeland et al., 2003).
In figure 4.1 we show a 30-day and 90-day moving window or rolling volatility, for log SMP, for
year 2011. A window of 30-day is also chosen in RAE’s reports, and compare this unconditional
volatility with the conditional one generated by the ARMAX/GARCH model described below.
30- and 90-Day Exponential Moving Average of SMPep for 2011
160
SMpep
30-day
140
90-day
Euro/Mwh
120
100
80
60
40
20
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Days
Figure 4.1: Dynamics of SMP ex-post for 2011(actual and 30-day and 90-day smoothed
values by Exponential moving average of daily data) (Source: ADMIE S.A).
23
Table 4.1: 30-Day, m=30, Annualized Volatility for ex-post SMP returns
2009
Annualized
Volatility
Volatility *
2010
Annualized
Volatility
Volatility
2011
Annualized
Volatility
Volatility
Min
0.094
0.32
0.084
0.29
0.121
0.41
Max
0.220
0.76
0.280
0.97
0.291
1.01
Mean
0.154
0.53
0.180
0.62
0.184
0.64
std
0.026
0.09
0.037
0.13
0.039
0.13
*Annualized volatility = σ *
where we assume 365 trading days in GEM and m is the length
of moving window.
However in the simple MA model, the moving averages are equally weighted (last day’s return
is equally weighted with the returns one week ago). In this “historic” model and all variations
are due only to the differences in samples, i.e. a short moving average window e.g. m=10 days
will be more variable than an m=30 one. But no matter which m is used, a simple rolling
volatility model estimates the unconditional volatility which is just one number, a constant,
underlying the entire series. In this model the wrongly perceived time variation in volatility is
in reality a sample variation and there is no stochasticity estimation. No dynamic evolution of
returns is taken into account by this model.
The equal weights on each return data are responsible for the appearance of “ghost features” in
the volatility series. Therefore, instead of using a simple, rolling moving average model we use
an exponentially weighted moving average (EWMA) that eliminates the “ghost features”. A
EWMA is written as follows:
(4.1)
where λ is a smoothing constant. The larger the value of λ the more weight is placed on past
data, the more smoother the series becomes.
Model (4.1) is used by JP Morgan-Reuter’s Risk MetricsTM (J.P Morgan/Reuters, 1996)
extensively in estimating volatility in financial assets (for daily data λ=0.94 is used). A careful
look on (4.3) shows that (4.1) is actually a model for the conditional volatility. In fact, model
(4.1) applied on squared returns is equivalent to a non-stationary GARCH model (see formula
4.7) IGARCH (Integrated GARCH), where k=0 and A1+G1=1. So, in order to compare the
conditional volatility estimation by our best found ARMX/GARCH model, describe in section 6,
with a “historic” EWMA model that also estimates conditional volatility, we construct an EWMA
model which can produce as close as possible the behavior of our GARCH model. We use
λ=0.94, as it is suggested by Risk MetricsTM (Risk MetricsTM , 1996), in the technical document,
equal to the persistence coefficient G1, (the moving window length or lagged time period in
24
EWMA is 77 days for 1% tolerance level). The dynamics of the generated conditional volatility
series matches extremely close the GARCH’s model dynamics, although differences in the levels
is observed, as expected due to differences in model specification.
Large G1 indicate that shocks to conditional variance take a long time to die out, so volatility is
“persistent”. Large A1 mean that volatility is quick to react to market movements and volatilities
show to be more “spiky”. Even though there are differences in volatility values produced by the
two models, their dynamic behavior is very similar (see fig. 4.7 for more details).
% Conditional Volatility from EWMA (λ=0.94) for SMP log returns
35
Volatility
3.65 min
34.57 max
16.12 mean
5.95 std
30
% Conditional st.dev
25
20
X: 2875
Y: 15.36
15
10
5
0
2004
2005
2006
2007
2008
2009
2010
2011
Figure 4.3 Conditional volatility estimated by EWMA model (λ=0.94)
Figure 4.4 shows the conditional correlation between SMP and load , the most significant driver
of the volatility of SMP as the table of the coefficients of the fitted model shows. A very
interesting point here is that the conditional co-movement of these two variables, reflected
through their conditional correlation is gradually reduced after 2008, the year of the country’s
recession starts.
25
Conditional correlation estimated by EWMA (Λ=0.94) of Load and SMP returns
1
Cond Correl
0.15 min
0.92 max
0.66 mean
0.124 std
0.9
0.8
Correlation Coefficient
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2004
2005
2006
2007
2008
2009
2010
2011
Figure 4.4 Conditional correlation between load (demand) and SMP estimated by EWMA model.
4.4 ARMAX/GARCH time Series Models for SMP
Volatility forecast models of the GARCH family are in general use. ARCH (Autoregressive
Conditional Heteroskedasticity) of Engle (Engle R.F., 1982) was the first model but the
generalized ARCH or GARCH (Bollerslev T., 1986) is the common denominator for most
volatility models. Let’s symbolize System Marginal Price, SMP by Pt . We take the logPt as the
only transformation. We treat Pt as a stochastic process exhibiting a degree of correlation from
one measurement to the next. We can exploitate this correlation structure found in our data, to
predict future values of the process based on the past history of observations. Exploitation of
the correlation structure provides us with an opportunity to decomposing Pt , into the
following components: a deterministic component or the forecast (a term used from now
on), a random component (the error or uncertainty, related to the forecast).
So, the general expression of the model for logPt is:
logPt = f(t-1,X)+εt
(4.2)
where f(t-1,X) is a nonlinear function representing the forecast or deterministic component, of
the current price as a function of the information set available at time t-1, Ψt-1. The forecast
may consists of past disturbances { εt-1, εt-2, ….}, past observations { Pt-1, Pt-2 , ….}, and any other
relevant explanatory time series data X (e.g. Load, Temperature, fuel prices etc.). { εt} is a
random innovation process, representing disturbances in the mean of { Pt }, but εt can also be
interpreted as the one step ahead or the single-period-ahead forecast error, since from (4.2) we
have
εt= Pt - f(t-1,X)
26
It is also assumed in this study that the innovations εt are random disturbances with zero mean
and uncorrelated from one time step to the other, i.e. E{εt}=0, E{εt1 εt2}=0, t1≠t2 .
Although εt are uncorrelated they are not independent but successive values depend on each
other as in case of a generating rule εt
εt = σt zt
(4.3)
where σt is the conditional standard deviation and zt is a standardized, independent,
identically-distributed (iid) random sample generated by a Normal or Student’s t probability
distribution.
Equation (4.3) says that {εt} rescales an iid process {zt} with a conditional standard
deviation, σt, that includes the serial dependence of the innovations. This means that the
quantity, εt/σt, the standardized disturbance, is also iid.
It is well known from finance theory that GARCH models are consistent with the concept of
efficient market hypothesis (EMH), according to which observed past returns cannot improve
the forecasts of future returns (Campbell Y.J., et.al, 1997). Therefore, GARCH innovations { εt }
are serially uncorrelated.
4.4.1 Conditional Mean Models
Since we are interested in modeling the impacts of a variety of explanatory variables on SMP ,
both of a “fundamental” type of relation to SMP (e.g. load, fuel prices, type of generation etc.)
and of “external” type (the regulator’s changes or policies), we adopt an ARMAX model for the
conditional mean, as given in (4.4)
The expression for the nonlinear function f(t-1,X) can take the general form of an ARMAX(R, M,
Nx) model for the conditional mean:
where φi the autoregressive coefficients, θj the moving average coefficients, εt innovations (or
residuals) a zero-mean white noise process with variance σ2, εt WN (0, σ2). X(t,k) is an
explanatory regression matrix of k variables. R, M are the orders of the Autoregressive and
Moving average polynomials and Nx the number of explanatory variables in the matrix X.
4.4.2 Conditional Variance Models
The conditional variance of innovations is given below:
Vart-1(logPt) = Et-1(εt2) = σt2
(4.5)
We must point out here the distinction between the conditional and unconditional variances
of {εt}. Conditional variance implies explicit dependence on a past series of observations.
Unconditional refers to long-term evolution of a time series and assumes no explicit
knowledge of past observations.
27
Following a similar approach with Lo and Wu (Lo K.L. and Y.K. Wu, 2004), let εt a real-valued
discrete-time stochastic process, ψt-1 the information set of all information through time t-1,
and σt2 the conditional variance. The general GARCH (P,Q) model for conditional variance of
innovation is
Εt |ψt-1 ~ N(0,σ2t)
(4.6a)
(4.6b)
where k>0, Gi≥0 and Aj≥0
This is a symmetric variance process i.e. it does not take into account the sign of the
disturbance.
Gi is a key persistence parameter of which high value implies a high impact of past volatility
to future volatility, while a low value implies a lower dependence on past volatility. Volatility is
said to be persistent if today’s return has a large effect on the future or forecasted variance
many, say, days ahead. This is equivalent in saying that periods of high and low volatility tend
to be grouped or clustered. The significance of Gi will be shown in section 10.1.6 below.
When P=Q=1 in (4.6b) we get the GARCH(1,1) model, and for R=M=0 and no explanatory Matrix
X , we have a constant mean equation (f(t-1)constant) and normally distributed innovations.
This simple model has been shown to capture the volatility in most of financial returns (see Lo
et. al, 2004 and references in it). We used this model in this work to test if it can do the job in
SMP series.
εt |ψt-1 ~ N(0,σ2t)
logPt = c+εt
2
σ t= k + G1σ2t-1+A1ε2t-1
(4.7a)
(4.7b)
(4.7c)
Generally, this model satisfies the stylized facts of persistence (or clustering) and mean
reverting. G1 + A1 is a point estimate of persistence, i.e. the time taken for volatility to move
halfway back to its unconditional mean value following a given perturbation. If G1 + A1 <1 then
we have a mean reverting conditional volatility mechanism in which perturbations or shocks
are transitory in nature. The closest this parameter is to unity the slower the shocks to SMP
volatility die out. The number of days for volatility to return or revert half-way back to its mean
is given as ln(1/2) / ln(G1 + A1). We have calculated this half-life parameter as described
below. The asymptotic relationship of the unconditional σ2 with the conditional one given by
(4.7c) is
=
.
The logPt series, in (4.7), consists of a constant plus an uncorrelated white noise disturbance ε t.
The variance forecast, σ2t-1, is the sum of a constant k plus a weighted average of last period’s
forecast and last period’s squared disturbance. As we have seen in section 2, the logPt, exhibit
significant correlation and persistence. Thus, our data for logPt is a candidate for GARCH
modeling and we have already mentioned that exhibit volatility clustering. We will investigate
whether the innovations of the fitted model to the logPt have an asymmetric impact on the
price volatility. It is rational to expect that positive shocks to SMP increase volatility more than
negative shocks. This rationality stems from the fact that an increase to SMP (a positive shock)
corresponds, naturally, to say, an unexpected increase in demand for electricity. Furthermore,
because marginal costs are convex, positive demand perturbations have a larger influence on
price changes relative to negative perturbations. The above situation describes the leverage
effect that we mentioned earlier and is captured in finance by the EGARCH model of Nelson
(Nelson D.B., 1991).
28
One type of GARCH model useful in capturing the leverage effect (or asymmetric volatility
effect) is the general EGARCH(P,Q) model, for the conditional variance of the innovations.
(4.8a)
where
for normal distribution and
for student’s t distribution with degrees of freedom v>2. Lj is the leverage term.
For the EGARCH(1,1) the Conditional Variance equation becomes
(4.8b)
where L1 is the asymmetry parameter. We note also that the magnitude effect is measured
by
and the sign effect is indicated by
.
If L1 = 0, then there is no asymmetric effect of past shocks on current variance.
If -1<L1<0 then a positive shock increases variance less than a negative shock.
If L1<1 then positive shocks reduce variance while negative shocks increase variance.
Parameter estimates for (4.8b) were found to be not significant, in our case. For this model
(4.8a) the approximate relationship between the unconditional variance σ2, of the fitted
innovations process, and the G1 parameter is
.
Another model that is used for capturing the leverage effect is the general GJR(P,Q) and
For P=Q=1 we have the GJR(1,1) with an equation for the conditional variance as follows
σ2=k+Α1ε2t-1+L1St-1ε2τ-1+G1σ2t-1
(4.8c)
where st-1= 1 if εt-1<0 and 0 if εt-1≥0
The variable st-1 is an indicator variable to account for the effect of positive shocks or good
news (εt-1≥0) and the negative shocks or bad news (εt-1<0) in the market. Therefore, the effect
on volatility of good news is A1 while in the case of bad news the effect is A1+L1. In this model
also, K is positive and A1 nonnegative (to ensure a positive variance. The EGARCH and GJR
models are asymmetric ones that capture the leverage effect, or negative correlation, between
rt and σ2t. This means that these models explicitly take into account the sign and magnitude of
the εt, the innovation noise term. Therefore if the leverage effect does indeed hold, the leverage
coefficients Lj should be negative for EGARCH models and positive for GJR. The terms Gi and Ai
capture volatility clustering in GARCH and GJR models while in EGARCH model volatility is
captured only via Gi terms.
29
4.5 Model specifications, outputs and diagnostic tests
We have tested a number of promising (composite) symmetric and asymmetric models in
searching for the best one to capture successfully the stylized facts in model’s innovations.
Table 4.2a show the results, the Akaike and Bayesian Information Criteria (AIC, BIC) and the
Durbin-Watson statistic. The model in (4.7) was found to be inappropriate (in replicating the
dynamics of SMP) by using a combination of criteria for assessing model’s specification. Yet,
this model can’t be used to detect the effects of fundamental and regulatory factors on SMP.
Model 10 seems to be is the best of all in the set of symmetric and asymmetric models since a
combination of AIC and BIC criteria , DW and the ARCH test for detecting any remaining serial
correlations in the residuals of the variance equation, are in favor of this model. Durbin –
Watson (DW) statistics is used to analyze whether the residuals are clean, i.e. tests the
hypothesis that there is no first-order autocorrelation or serial correlation apparent in the
residuals. The residuals must be clean and have no structure. If 2<DW<4 then there is negative
correlation in the residuals while for DW<2 positive correlation. As a rule of thumb, a DW of
exactly 2 indicates clean residuals and any substantial deviation from this value indicates 1 st
order serial correlation in the residuals. Model 10 in table 4.2a, which is our best found model
has DW=2.036 close to the perfect value so we can trust our model of not having first order
serial correlations in the residuals. The existence of higher order serial correlation is detecting
through ARCH test, and the correlograms of standardized residuals square (Ljung-Box QStatistics), as described below.
The specification of our best model 10 is therefore ARMAX(7,1,25)/GRCH(1,1). The complete
form of the system of equation of the model is:
conditional mean (equation (4.4))
logPt = c + φ1 logPt-1 + φ2 logPt-2 +....φ7 logPt-7 +θ1εt-1 + β1Χ(t,1) + β2Χ(t,2) +……+ β25 Χ(t,25)
(4.9a)
conditional variance
=k+Α1ε2t-1+G1σ2t-1
(4.9b)
The results of fitting the model to our data are given in table 4.2a, where the values of the
coefficients are provided.
30
Table 4.2a: Assessment of model specifications by applying AIC ARCH test
Model
Conditional
Volatility
equation
Specification
Number of
Exogenous
Regressors
mean
equation
Rsquared
variance
equation
DurbinWatson
Stat
AIC
HIC
Hannan
- Quinn
ARCH-test (for
7 lags)
ARCH
TEST
(serial
correlation
remains in
Stat.
pvalue
residuals
Yes/No)
ARMAX(0,0,0)/GARCH(1,1)
Base model
0
0
-0.097
0.189
0.409
0.417
0.412
106.20
8
0.0000
yes
1
ARMAX(1,1,25)/GARCH(1,1)
25
0
0.916
1.818
-1.886
-1.820
-1.862
12.255
0.0925
no
2
ARMAX(1,1,25)/GARCH(1,1)
25
8
0.852
0.780
-1.415
-1.338
-1.387
41.441
0.0000
yes
ARMAX(1,1,25)/GARCH(1,1)
25
25
0.853
0.792
-1.432
-1.320
-1.392
48.093
0.0000
yes
4
ARMAX(2,1,25)/GARCH(1,1)
25
25
0.917
2.068
-1.966
-1.848
-1.924
31.912
0.0000
yes
5
ARMAX(2,1,25)/GARCH(1,1)
25
8
0.919
2.058
-1.932
-1.847
-1.901
26.674
0.0004
yes
6
ARMAX(1,1,25)/GJR(1,1)*
25
25
0.851
0.790
-1.434
-1.320
-1.393
47.343
0.0000
yes
ARMAX(2,1,25)/GJR(1,1)*
25
8
0.919
2.070
1.9327
-1.847
-1.901
26.712
0.0004
yes
ARMAX(2,1,25)/EGARCH(1,1
)*
25
8
0.919
2.050
-1.930
-1.845
-1.899
30.658
0.0001
yes
ARMAX(7,1,25)/GARCH(1,1)
25
25
0.918
2.074
-1.966
-1.835
-1.910
19.600
0.0065
No
ARMAX(7,1,25)/GARCH(1,1)
25
8
0.921
2.036
-1.971
-1.878
-1.938
13.331
0.0644
no
0
3
7
symmetric
symmetric
asymmetric
8
9
symmetric
10
Note*: leverage effect coefficient found to be non-significant, see table 4.2b
31
Table 4.2b: Asymmetric model coefficient of leverage effect
Model
6
7
8
L1
0.1268
0.0843
-0.0048
p-value
0.1385
0.3046
0.8892
Table 4.3 : ΑRMAΧ(7,1,25)/GARCH(1,1) model parameters
Mean Equation
Variable
Coefficient
Coeff. value
Std. Error
z-Statistic
Prob.
1.419068
-0.529789
0.1559
0.5963
C
D(AHELENR)
β1
0.637868
-0.000071
0.449498
0.000136
D(ALIAKENR)
β2
-0.001604
0.000741
2.163641
0.0305
D(ARAXTHENR)
β3
-0.000245
0.000862
-0.284382
0.7761
LOG(BRENT)
β4
0.256842
0.077274
3.323766
0.0009
LOG(HFOG)
β5
0.005906
0.002383
2.477875
0.0132
LOG(HYDGEN)
β6
-0.052671
0.006899
-7.634190
0.0000
LOG(HYDMR)
β7
-0.028504
0.005643
-5.050850
0.0000
D(LADONENR)
β8
-0.003870
0.002852
-1.357035
0.1748
LOG(LIGNG)
β9
-0.336946
0.025724
-13.09859
0.0000
LOG(LOAD)
β10
1.558140
0.031401
49.62039
0.0000
LOG(NATGASG)
β11
0.047442
0.007023
6.755063
0.0000
D(NESTOSENR)
β12
0.002768
0.001042
2.655939
0.0079
D(PLASTENR)
β13
-0.005011
0.001603
-3.124855
0.0018
LOG(RESGEN)
β14
-0.033070
0.002008
-16.47227
0.0000
LOG(TOTEXPORTS)
β15
0.023108
0.002264
10.20810
0.0000
LOG(TOTIMPORTS)
β16
-0.127141
0.010479
-12.13301
0.0000
LOG(UAVAI)
β17
-0.714757
0.032649
-21.89196
0.0000
RΜR1
β18
0.176995
0.094799
1.867053
0.0619
RΜR2
β19
0.161638
0.099196
1.629483
0.1032
RMR3
β20
0.234799
0.106144
2.212081
0.0270
RMR4
β21
-0.151792
0.025032
-6.063320
0.0000
RMR5
β22
0.262312
0.044900
5.842120
0.0000
RMR6
β23
-0.364146
0.041763
-8.724973
0.0000
RMR7
β24
0.107159
0.045132
2.374328
0.0176
RMR8
AR(1)
β25
φ1
0.130810
0.236197
0.103499
0.140190
1.63875
1.684830
0.2063
0.0920
AR(2)
φ2
0.203822
0.070729
2.881717
0.0040
AR(3)
φ3
0.088161
0.025150
3.505458
0.0005
AR(4)
φ4
0.078068
0.023089
3.381118
0.0007
AR(5)
φ5
0.087547
0.021817
4.012843
0.0001
AR(6)
φ6
0.069808
0.022847
3.055447
0.0022
AR(7)
MA(1)
φ7
θ1
0.139523
0.241577
0.020427
0.141563
6.830459
1.706500
0.0000
0.0879
32
Variance Equation
K
RESID(-1)^2
GARCH(-1)
RMR1
RMR2
RMR3
RMR4
RMR5
RMR6
RMR7
RMR8
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
A1
G1
0.921336
0.920421
0.105753
31.70594
2873.546
2.036971
0.001466
0.134847
0.787272
0.000512
0.000942
-0.002166
8.27E-06
0.000237
0.000411
0.000356
0.000619
0.000330
0.020387
0.026990
0.000530
0.003153
0.003153
7.21E-05
0.000135
0.000199
0.000279
0.000823
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
4.440105
6.614217
29.16894
0.096472
0.298736
-0.690960
0.114690
1.755964
2.063805
1.275853
0.752420
0.0000
0.0000
0.0000
0.9231
0.7651
0.4896
0.9087
0.0791
0.0390
0.2020
0.4518
3.977355
0.374881
-1.971799
-1.878290
-1.938088
Therefore, the conditional variance equation becomes:
σ2t =0.0011 + 0.134ε2t-1 + 0.787σ2t-1
(4.10)
If we interpret G1 and A1 as weights, A1 indicates that a weight of 13.4% is assigned to the most
recent observation. (4.10) clearly shows that volatility is time varying, responding to the most
recent data value of SMP. A weight of 79% is attached to the volatility estimate of yesterday.
The persistence parameter is given by
i.e. the model is covariance
stationary. This parameter shows also the existence of a volatility clustering or mean
reverting behavior of the SMPep. The Half-life parameter is H=ln(1/2)/ln(G1+A1)=9 days,
meaning that it takes on average 9 days for half of the volatility shock to fade out.
We have to mention here that a formal leverage effect as opposed to inverse leverage effect as
Knittel and Roberts (2005) and Karakatsani and Bunn (Karakatsani N., et.al., 2004) have
reported in their work, where a positive shock will increase the volatility more than a negative
one. Our finding is that we do not have any leverage effect since the corresponding coefficients
L in the asymmetric model fitting were found to be not significant. The result, however,
reported in the work of Gianfreda (2010) for French, German, Italian and Spanish markets,
using an EGARCH(1,1) model, and in the work of Montero et. al (2011) has shown the existence
of such leverage effects.
The final value of the conditional st.dev or volatility σt (see fig.4.8), is 0.133. We compare this
value to the unconditional standard deviation σ, estimated by the model’s parameters as
follows:
Therefore, the long-term behavior of σt forecasts tends to the unconditional volatility of 0.133
given by using the parameters of the estimated model.
33
Figure 4.6 shows the actual, fitted and residuals (innovations) values of model (4.10) while
figure 4.7 depicts the Conditional Variance generated by the same model. On the same figure we
provide the dates the regulatory reforms took place, so we can see the spikes or shocks they
have induced on the conditional volatility of SMP, as the coefficients in mean and variance
equations associated with these dummy variables (reforms) reveal in table 4.3.
Model ARMAX(7,1,25)/GARCH(1,1) fitting results on logSMPep data.
(Fitted and actual values right scale, residuals left scale)
5.2
4.8
4.4
4.0
3.6
.6
3.2
.4
2.8
.2
.0
-.2
-.4
-.6
-.8
2004
2005
2006
2007
Residual
Figure 4.6 :
2008
2009
Actual
2010
2011
Fitted
ARMAX(7,1,25)/GARCH(1,1) fitting results. Plot of actual, fitted and residuals
(innovations).
Conditional Volatility of log SMP
.30
RMR1
Oct 2005
Conditional st.dev
.25
RMR2&3
1 & 13 Jan 2006
RMR5
01 May 2008
RMR8
01 Sep 2011
.20
RMR7
30 Sep 2010
RMR6
01 Jan 2009
.15
RMR4
01/04/2007
.10
.05
.00
Unstable pre-mature
phase of high Volatility
2004
2005
Escalated Volatility phase
Tranquility phase
2006
2007
2008
2009
2010
2011
Figure 4.7 Phases of evolution of Conditional volatility of log SMP and dates of RMRs.
The most tranquil phase of the market, in terms of volatility, is from May 2006 to April 2008.
34
This calmness, however, is broken due to (among other factors) reform 4, generating the
second significant spike in this period. The end of this tranquillity comes when reform RMR5 is
launched in May 2008, responsible for a high spike taking the volatility from a value of 5% to
22.5% , to drop again to the previous value after a month, passing first through the
unconditional value of σ=13% (the long-term mean value), the volatility Shock having lost half
of its intensity in almost 10 days (half-life was estimated to be 10 days). After the launching of
RMR5, a phase of upward systematic escalation of the conditional volatility begins, with
relatively small (compared to the previous spikes) spikes due to reforms 6 and 7. RMR8 gives
the last spike shown but this can’t be attributed to this reform due to the fact that the
coefficient found is insignificant. In this escalation period the conditional volatility is increased
from 5% to 13.5% (170%).
35
% Conditional st.dev
30
25
20
15
10
5
0
2004
2005
2006
2007
2008
2009
2010
2011
EWMA Volatility of smp returns VOLAT
ARMAX/GARCH model Volatility
Figure 4.8: % Comparing dynamics of
ARMAX(7,1,25)/GARCH(1,1) and EWMA models.
Conditional
Volatility
estimated
by
Figure 4.8 shows the comparison of the forecasted conditional volatility of the GARCH model,
versus the conditional volatility estimated EWMA. This comparison serves as an indication of
the model’s ability to track the variations in the GEM’s volatility. The asymptotic behaviors of
the two models forecasts approach a long-term value of 13.4% (the last value red curve) while
and 15.3% for the blue curve. Both models exhibit almost the same dynamic behavior , however
EWMA model show instantaneous values always larger than GARCH due to differences in A 1
(GARCH) and λ-1= A1 (for EWMA) parameters.
35
Sample Partial Autocorrelations
Sample Autocorrelation
Autocorrelation Function of squared standardised residuals
1
0.5
0
-0.5
0
1
0
1
2
3
4
5
6
7
8
Lag
Partial Autoc. Function of squared stand. residuals
2
3
4
9
10
9
10
1
0.5
0
-0.5
5
Lag
6
7
8
Figure 4.8 Autocorrelation and Partial autocorr. Functions Of standardized squared
Residuals of model (4.9).
Any successful GARCH model is that one in which there is no autocorrelation in the squared
standardized returns εt2/σt2, meaning that the model is capable of capturing volatility
clustering in the original returns. Volatility clustering implies a strong autocorrelation in
squared returns.
From fig. 4.8 we see that the standardized squared residuals show no correlations (compare
with ACF and PACF of SMP in fig. 3.6 before fitting the model). Therefore, our fitted model
sufficiently explains heteroskedasticity behavior in our data.
Furthermore, we repeated ARCH-test on these innovations (Table 4.4) and compared the
results with those in the pre-estimation analysis. In the pre-estimation analysis the test
indicated the existence of both correlations and heteroskedasticity. In the post-estimation
analysis, ARCH-test now indicates acceptance of the respective null hypothesis that no ARCH
effect exists, up to lags seven. This result further enhances the explanatory power of the fitted
model. The ARCH test statistics was found to be 13.33 and insignificant (p=0.0643) for seven
lags (all coefficients at lags 1 to 7 are insignificant. So no ARCH effects exist in the innovations
of the fitted model.
36
Q-Q plot of residuals vs Students-t distribution.
.8
Quantiles of Student's t
.6
.4
.2
.0
-.2
-.4
-.6
-.8
-.8
-.6
-.4
-.2
.0
.2
.4
.6
Quantiles of innovations of model 10
Figure 4.9 Q-Q plot of model’s residuals vs the Student’s-t distribution.
Figure 4.9 shows the result of fitting the residuals generated by the model on the theoretical
Student’s-t distribution that we have chosen to be the distribution of errors in specifying the
GARCH(1,1) model. We see a very good fit of the residuals since the largest amount of data
are on the theoretical line, except the extreme right, positive values that deviate from the line,
forming a fat tail of the distribution of the residuals. This fitting of good quality is also an extra
evidence that our model has been correctly specified. Using now our best model (4.9,4.10) we
perform in-sample or static SMP forecasts as shown in figure 4.10 , the dynamics of which
mimics very well the dynamics of the actual series in fig. 3.3. The quality of the fit is also very
good: Theil’s coefficient 0.045 , Bias (mean) and variance proportions small (0.003 and 0.022
respectively). The descriptive statistics of the forecasted series are very close to the ones of the
actual series (mean 57, max 147, min 20.3, st.dev 19.51, skewness 0.52,kurtosis 3.12), by
comparing with the values in table3.3.
37
In sample Forecasts of SMP
160
140
120
Euro/Mwh
100
80
60
40
20
0
2004
2005
2006
2007
2008
2009
2010
2011
Figure 4.10 In-sample forecasts of SMP ex-post from best model
In figures 7.2 and 7.3 we show the forecasting results of the model corresponding to two
different scenarios for the evolution of the conditional variance with different starting times :
the first in the tranquil, of low volatility phase, just before the application of RMR5 (end of April
2008) , while the second in a high volatility regime, namely on 4th May 2008 three days after the
enactment of RMR5. In the first case the long-term stable value of unconditional variance is
approached from below while in the second case from above. These two scenarios confirm the
quality of the model in generating rational and consistent dynamic behavior of the conditional
volatility.
38
200
SMP Forecast
± 2 S.E.
160
120
80
40
RMR5
1 May 2008
0
M1
M2
M3
M4
M5
M6
M7
M8
M9
2008
.007
Conditional variance evolution starting from a tranquil phase
(end of april 2008) approaching stable value (0.0069) from below.
.006
.005
RMR5
1 May 2008
.004
.003
M1
M2
M3
M4
M5
M6
M7
M8
M9
2008
Forecast of Variance
Figure 4.11 Conditional Variance evolution of SMP from end of April 2008 to end of September
2008.
39
200
SMP Forecast
± 2 S.E.
160
120
80
40
5
12
19
26
2
9
M5
.035
16
23
30
M6
Conditional variance evolution starting from turbulent phase
(4 May 2008) approaching stable value from above.
.030
.025
It takes 9 days for half
of the shock to fade out
.020
.015
.010
.005
5
12
19
26
2
9
M5
16
23
30
M6
Forecast of Variance
Figure 4.12 Conditional variance evolution of SMP from 4th May 2008 to 30 June 2008.
40
5. Interpreting the results
The mean equation
Referring to table 4.2b with parameter estimates of the Best Specified model 10, suggests that
our time series model confirms the sign and intensity of the effects of fundamental variables on
SMP as it is shown in a typical fundamental analysis.
All the quantitative fundamental variables, the autoregressive and moving average structures
are robust to controlling for regulatory changes in the GEM’s structure. Specifically, both the
signs and the values of the coefficients of the fundamental factors remain unchanged before and
after the inclusion of RMRs in the model specification.
we observe that hydro generation, both for must-run and for “normal” functioning, have a
negative and statistically significant impact on the evolution of SMP. The effect however of the
Hydgen factor is stronger than that of the hydmr (hydro must-run), as the values of the
estimated coefficient indicate. This is a logical result as the amount of hydro must-run
generated energy is a small part and is included in the series of the total hydro generation
(hydgen), used more intensively during peak-hour according to DAS (day-ahead schedule).
The scarcity of hydro generation in 2011 is, among other fundamental factors, responsible for
the SMP increase in this year, reflecting the strong and negative correlation of hydrog or
hydromr with SMP. Years 2009 and 2010 instead, were intensely wet, causing a downward
force on SMP. However, the driest years were 2007 and 2008 exerting a significant negative
‘pressure’ on SMP.
The significantly reduced hydro generation in 2011 exerted an upward trend on SMP, mainly
due to the need for substitution by more expensive energy (see the negative correlation
coefficients of hydgen with the thermal generation factors, brent, hfog, ligng, and natgas).
How much significant is the factor Hydrogen in the formation of SMP (through the level and
allocation profile of hydro generation), is also shown from its contribution to the formation of
SMP’s “by-product”, the retail margin. A conservative, for example, water management i.e.
over-restrictive in particular time periods, can produce a reduction in retail margin, favoring in
this way a market supplier that happened to have a reduced retail volume. Therefore a supplier
in the retail market with large share and an ability to control hydro generation, as PPC in
Greece, can have a crucial impact not only on SMP formation but also, in consequence, on the
retail price.
The control over hydro generation factors can be done by designing a new approach of
managing hydro stations by considering aspects such as the opportunity cost of water, the cost
of fuel mix substituted by water and by a close linking of the above factors to the level of
reservoirs.
A negative effect on SMP have also the production of RES (resgen) and Lignite (lignitegen)
stations with different relative strengths as the values of their corresponding coefficients
reveal. A careful examination of the evolution of the share of each type of generation in the total
annual installed capacity as well as in the duel mix generation, as it is shown in Tables 2.1 and
2.2, reveals that RES share generation is always less than that of hydro as well as Lignite
stations over the period 2004-2011, for each year.
The higher the production by lignite stations the lower the SMP, reflecting the impact of a low
price input factor to the generating portfolio of the system. Negative, also, effect on SMP have
the total emported energy (totimports) and the generating unit availability (Uavail). The
factor has the next higher coefficient but now with a negative impact on SMP is Unit availability
for (uavail) since an 1% increase in this variable, ceteris paribus, reduces 0.71% the value of
SMP. Planned and unplanned outages for maintenance reduce availability. Unplanned outages
41
are stochastic events distributed uniformly over the year. Efforts are made so planned outages
are scheduled to happen during periods of low load and low SMP. The more available are the
generating units the lower the SMP, since enough of the required capacity is readily available
and according to the DA and dispatching schedules (the units have hardly competing each other
to be included on the list for next day’s generation). More specifically Unit availability (uavail)
depends on the level of outages and maintenance and is negatively related to SMP. For example,
in the end of 2011 two severe outages in IPP’s plants and one in a Unit of PPC (Lavrio5) induced
these Units unavailable for long periods of time. The induced, due to this fact cuts in demand,
exerted an upward pressure on SMP. During June of the same year a labor Union strike at PPC
caused a major capacity withholding i.e. forced power cuts, reducing availability in 20
generating Units which in turn had an extremely strong upward escalation of SMP (the price
escalated from 42 €/MW in 19.06.2011 to the price cap (an administratively set price) of 150
€/MW in 24.06.2011 and finally to 148€/MW in 29.06.2011, being on average at 139.7 €/MWh
for these ten days).
Positive effect on SMP has the 3-month moving average of Brent Oil price (Brent) and the
generation of Stations that use Heavy fuel Oil (Hfog), an expected result. The higher the values
of these two variables, the higher the SMP. The energy production of Natural Gas (natgasg)
Stations also have a positive influence on the behavior of SMP, as this type of fuel is an
expensive production input. The extent of natural gas’s impact on SMP is reasonable , taking
into consideration the share of this fuel in the generation mix (see tables 2.1 and 2.2) . Yet, the
positive coefficient reflects the strong correlation between SMP and Natural Gas prices and
more precisely corresponds to the SMP-GAS prices spark spread8, defined here as the
difference between SMP and daily Balancing price of gas (see figure 5.1). The escalation of
spark spread volatility to increasing values is evident after the second quarter of 2010, exerting
a positive effect on SMP. The reforms in the market may have broken this positive co-variation,
a fact difficult to be captured by the model by only considering changes in the levels of these
two quantities. Figure 5.2 shows the percent change (annual rate) of monthly SMP versus
Natural Gas prices. The spikes in spark spread, SMP ex-post and SMP Das observed in the
quarters shown in the graph reflect the strong positive co-movement of these series.
Natural Gas Price vs SMP price in GEM Sep 2008-2011
100
90
80
Euro/Mwh
70
60
50
40
30
20
10
III
IV
2008
I
II
III
2009
IV
I
II
III
IV
2010
I
II
III
IV
2011
SMPep_monthly_avg
Balancing_Prics_month_avg
SMPdas_monthly_avg
Import_price_ngas_avg
Spark_spread
We have used monthly weighted-average import price (WAIP) and the daily balancing gas (HTAE) for the same
months, given in DESFA’s internet site from Jan 2009 to Dec 2011. The data are also available in RAE’s website. As
spark spread here we mean the difference of SMP and Balancing price of Nat gas.
8
42
Figure 5.1 Monthly average Nat Gas price versus SMP in GEM (Sep. 2008-11).
% Change (Annual rate) of SMP vs Nat Gas prices
50,000
% change
40,000
30,000
20,000
10,000
0
III
IV
2008
I
II
III
IV
I
2009
%
%
%
%
%
Change
Change
Change
Change
Change
II
III
2010
(Annual
(Annual
(Annual
(Annual
(Annual
IV
I
II
III
IV
2011
Rate) SMP-ExP_month
Rate) SMP_DAS_MONTH
Rate) BALANCING_PRICE_NGAS
Rate) IMPORT_PRICE_NGAS
Rate) SPARK_SPREAD
Figure 5.2 % change (annual rate) of SMP and Nat Gas prices in GEM (Sep. 2008-11)
The total export of energy (totexports) increase SMP as expected, a rational outcome as energy
extracted from the system reduces the supply for domestic usage. The heaviest positive impact
on SMP comes from Load i.e. the total demand of all customers of the system. The larger the
demand (i.e. the further shift to the right of the demand curve) the much higher the new
equilibrium point i.e. the point of intersection of Supply and Demand Curves. The coefficient
corresponding to load has the largest value indicating that SMP is mostly driven by this
variable, as it is well known also through models based on fundamental analysis. So, an increase
of 1% in the daily demand, over the period of our analysis, leads to a multiple increase, ceteris
paribus, in the level of SMP of 1.56%. An example enhances the view of this strong positive
dependence. In November 2011, load (demand) increased of about 8% compare to the
previous year same month, due to an increased usage of air-conditioning for heating (oil was
considered a more expensive alternative to electricity for households), causing an upward
pressure to SMP ( i.e an 8%x1.56%=12.5% increase in SMP).
An increase of 1% in the Brent Oil price will result, on the average, in an increase of 0.25%
while a similar increase in the level of production by a station using heavy fuel oil is
accompanied by a positive and negligible increase in SMP (0.006%). This result is in accordance
with the relatively very small share (on the order of 5% to 6% each year) of this type of
generation, as shown on Table 2.1.
The need for linking hydro generation patterns to reservoir levels is further enforced by
considering their strong correlation with the corresponding energy reserves that are strongly
and negatively correlated with SMP (see correlations table in the Appendix 4).
A combination of factors occurring concurrently can have a significant impact on SMP, even
reducing it to almost zero level. For example, a significant drop in load (demand), as in Easter
holiday, combined with compulsory generation quantities due to renewables, Plant’s technical
minima and imports, can create an imbalance between production and consumption (an excess
generated quantity in our case). Due to this excess, imports can be offered at a zero value and it
is necessary to impose a minimum value (curtailed value) in this extreme situation. In 2009 we
have witnessed such an extreme case.
43
6. The Impacts of RMRs on SMP
The main message coming out the table 4.3 is that the regulatory interventions in the market
architecture have significantly affected the conditional mean of the SMP price and partially its
conditional volatility (only RMR6 at 5% level is significant). The results suggest that the
average SMP was affected by the regulatory reforms, ceteris paribus, with upward, downward
trends and spikes attributed to the signs and intensities of the found coefficients.
In the mean equation, the dummy variables representing the Regulatory Market Reforms, RMR,
were found to have a significant (most at a 1% level) effect on SMPep, except RM2 and RMR8
that found to have no impact. Positive impact have RMR1, RMR3, RMR5 and RMR7 and
negative impact RMR4 and RMR6. The highest positive impact on SMP is due to market
reformation RMR5 (value of coefficient 0.26) regarding the Cost Recovery mechanism, CRM
(see page 10 and the reference mentioned there). The next largest positive impact (0.23)
comes from RMR3 reform, regarding the first change of methodology of calculating system
marginal price (SMP).
It is pointed out here that this reform was not expected by the Regulator to have any significant
effect on the evolution of SMP (RAE 2010, and Kalantzis F., et.al, 2012). A very crucial point
here is that, in general, there are motives of Generators for a systematic abuse of CRM (in case
this mechanism is in place) that allows them to bidding below their marginal cost. This strategy
of Generators became possible after the launching of RMR6 which in combination with CRM
gave the Generators the opportunity to make extra profits, when SMP exceeded their cost (this
market rule allows a generator to offer 30% of its capacity at a price less than its minimum
marginal cost, while at the same time they can reap a retained compensation at this cost plus
10%). Therefore, the overall, combined, effects of RMR5 and RMR6 have a rather distorting
effect on the market. In the time of writing this paper, the authors were aware of RAE´s
intentions to propose measures to strongly reduce this distortion by changing or even
removing CRM. It turned out that RMR6 is a critical exogenous (relative to fundamental factors)
qualitative factor in shaping the dynamics of SMP. Even though this reform allows the dispatch
of various Units for providing reserves to the system (a crucial factor in securing Unit´s viability
in a period of excessive capacity), it heavily suppresses SMP to values not reflecting generation
cost. The negative effects of RMR5 and RMR6 on SMP have also crated two side effects. First,
due to suppressed SMP, and given the feed-in-tariffs mechanism on which RES producers are
compensated on a special levy level, the need for this purpose cash outflows increased
dramatically and secondly the creation of SMP values not corresponding to the ones expected
by the fundamental underlying operating variables of the system that governs SMP.
As far as the impact of RMR8 on SMP is concerned, coefficient β25 in table 4.3 was found to be
no significant. The Regulator however had expected an increase to SMP due to this reform. This
is due to the fact that the length of the data set after the date of enactment of this reform, Sept.
2011, is very small, therefore the effect on SMP of this dummy variable, on average, is
insignificant. However, having a look at the results of year 2011, we see that this tax, which
induced asymmetric effects on gas-fired electricity generation versus lignite and imports
(actually the variable cost of the gas plants increased 5.4 €/MWh), overall has induced a rise in
SMP. During the same year, 2011, the combination of this reform with a decreased Hydro
generation (represented by variable Hydrogen in the model) had, as a result, a sustainable SMP
rise, from the date of application of RMR8 onwards. More specifically, the daily average ex-post
SMP increased from 63.71 €/MWh on 31st August 2011 to 90.75 €/MWh on 1st September (+
42% ). In general, the average SMP during 2011 before RM8 was 65.00 €/MWh while after the
reform changed to 83.86 €/MWh. The average price in 2011 was 71.70 €/MWh compared to
52.25 €/MWh in 2010 (see table 3.3).
44
Comparable impact to the one by RMR3 has the reform RMR1 (0.177) which corresponds to
adoption of the mandatory pool (ex-post settlement) as the preferred electricity market model
in Greece. This reform that changed the methodology of estimating SMP, in combination with
RMR3, seems to have generated not an “additive” but a “multiplicative” effect. One natural
explanation is that before the enactment of those two reforms, SMP was determined mainly by
Lignite generating Units having an average marginal cost of about 27€/MWh, which offer the
implementation of RMR3 the same units determine SMP only during the period off-peak hours,
while at the same time Natural Gas and Oil Units (with a marginal cost of around 60€/MWh)
started to set SMP for largest time share during peak hours (almost 60% of total hours).
If we multiply the difference in marginal cost (60€/MWh - 27€/MWh = 33€/MWh) with the
time share 60% mentioned above we have a net effect of 33€/MWhX0.6020€/MWh.
Table 6.1: Impacts of Regulatory Reforms on SMPep
Market Reform with
significant impact
RMR1
RMR3
RMR4
RMR5
RMR6
RMR7
Coefficient
Value
% impact on SMPep*
β18
β20
β21
β22
β23
β24
0.1769
0.2347
-0.1517
0.2623
-0.3641
0.1071
15.35
25.86
-14.00
29.60
-30.50
11.30
*Note: the % impact of a RMRν dummy variable (changing for 0 to1), ceteris paribus, having a
coefficient βν is
.
Table 6.1 gives the impact of RMRs on SMP. For example, the SMP (ex post) value on the day of
application of RMR3 (January 13, 2006) was 41.04€/MWh. On next day, the price went to
49.36€/MWh i.e. an increase of 8.32€/MWh (20.3%), on January 15 went to 48.65€/MWh i.e.
an 18.54% increase and three days later, on January 16, the price increased to 52.05€/MWh, i.e.
26.82% close to 25.86%, as given in the table above. The market realized the impact (due to its
inertia) after 3 days.
Based on the above remarks and the entries in table 2.5, we observe that our model revealed
different effects of RMR6, RMR7 on SMP, than the Regulator’s expected ones. Should this
model had been available to the regulator before the launching of the reforms, it would be very
useful in providing a better picture on the expected effects of those reforms as well as on RMR4
and RMR5.
The conditional variance equation
From table 4.3 we see that the quantified effects of the reforms on the volatility of SMP are
negligible, except reform RMR6 which is significant at 5% level, however with negligible
magnitude (0.0004%). However, we must point out here that since the reforms affect
significant the average SMP returns and that the two equations are coupled (see system of
equations 6.10), these reforms affect volatility indirectly.
45
7. Comparing conditional volatility of SMP in GEM with SMP in other Markets
Table 7.1 shows the parameter estimates of the AR(1)/GARCH(1,1) model on SMP, applied in
various electricity markets taken from the work of Escribano et al. (2002), amended by the
results found in this work for the Greek electricity market and the work of Petrella (2012) for
the Italian market. So, we can compare the rate or speed of mean-reversion of the Greek
market with those in the paper. The factor A1+G1 expresses the persistence parameter of the
conditional volatilities to its mean value. In Financial markets it is common that G is larger
than 0.7 but A tend to be less than 0.25. If A+G is close to one then the persistence is high and
a shock in the series will decay slowly. A low persistence value i.e A+G<<1 leads to the fast
decay of the shock to its long-run volatility. If A+G=1 we have a non-stationary or nonstationary or Integrated GARCH model(I-GARCH) for which term structure forecasts do not
converge (there is no mean reversion)
Table 7.1: Variance equation parameters of GARCH(1,1) model applied in various markets
(source : Alexander C., 1998, Escribano et al., 2002, Petrella et al., 2012)
Financial Markets
Equities
UK
GE
US
JP
NL
USD rates
DEM
JPY
GBP
NLG
ESP
AUD
Index
ASE (Greece)
Electricity Markets
Greece
Italy
Spain
Nord Pool
Argentina
Australia (Victoria)
New Zeeland
PJM
A1
G1
0.105
0.188
0.271
0.049
0.146
0.810
0.712
0.641
0.935
0.829
0.915
0.900
0.912
0.984
0.975
11
7
8
43
28
0.113
0.102
0.028
0.125
0.160
0.241
0.747
0.763
0.935
0.735
0.597
0.674
0.860
0.865
0.963
0.860
0.757
0.915
5
5
19
5
3
8
0.100 0.900
1.00
Undefined
0.13
0.47
0.18
0.41
0.85
1.07
0.40
1.11
0.92
1.04
0.96
1.00
1.22
1.56
1.00
1.61
9
Undefined
17
Undefined
Undefined
Undefined
Undefined
Undefined
0.79
0.576
0.78
0.59
0.37
0.49
0.60
0.49
A1+G1 Half –life (days)9
In the markets of table 7.2, Nord Pool, Argentina, Australia, New Zeeland, Italy and PJM have
persistence parameter equal to one so there is no mean reversion. A low degree of mean9
Half-life is defined as log(0.5)/log(A1+G1)
46
reversion can be explained, according to Escribano, (2002), by the fact that in some of the
markets the proportion of electricity generated by hydro resources is extremely large, as in
Nord Pool (in the Greek market hydro share accounts for 24% of net installed capacity in 20082009, table 2.1). The expected inter-temporal substitution between inputs is more intense in
the markets with large amount of Hydro-generation than in the markets with low one,
indicating that hydro stations (reservoirs) play the role of the indirect storage of electricity. In
the other markets of the table we observe smaller persistence values indicating a higher degree
of mean-reversion since generators cannot use inventories to smooth out shocks. It takes nine
days in Greece and seventeen in Spain for the conditional volatility to return to their long-run
mean value. GEM in this respect behaves like the first three equities market while Spanish
market like the USD/GBP rates. We also point out here that mean-reversion in load (demand)
or in temperature are the main factors of causing the mean-reversion in electricity prices.
Wolak (1997) and Lucia and Schwartz (2002) have also shown that SMP are more “turbulent”
or volatile in markets dominated by hydroelectric power. Large dry periods result in significant
lower hydro generation, causing in turn an increase, on the average, in SMP. In general,
instability of weather conditions have a significant effect on the mean-reversion process
(actually its dynamics resembles a unit root process with autoregressive conditional
heteroskedastic errors).
The oligopoly microstructure of Greek electricity market (at least at its early stage) and the
particular rules in place for compensating the Generators, during the transitional period from
less oligopolistic to more competitive, are the main factors in the evolution of this different
market, compared to “mature” markets e.g. NordPool, Australia etc. (Escribano et al., 2002).
The way stranded costs are treated in a market creates conflictive incentives on the few
participating players (Federico G. and A. Whitmore, 1999). The interaction of incentives has
direct effects on energy price risk. There is a negative dependence between stranded costs to
be paid to generators and the price established in the pool. Actually, generators earn higher
profits from their participation in the pool, in the case that the prices are higher than a known
and pre-established level, but they will get a lower amount of standard costs. These conflicting
interests among generators (which depend on the market’s microstructure i.e. expectations on
the likelihood of receiving stranded costs, generator’s market share etc.) have a predictable
impact on the equilibrium price i.e. SMP.
Table 7.2 % Conditional Volatilities of log SMP and ASE Index
SMP log returns
max
min
mean
St.dev
ASE log returns
EWMA (λ=0.94)
ARMAΧ/GARCH
EWMA (λ=0.94)
ARMAΧ/GARCH
34.60
3.66
16.12
5.95
26.30
3.92
9.31
4.15
6.46
0.31
1.60
0.91
5.75
0.62
1.70
0.86
47
8. Conclusions
In the beginning of this work we stated its targets, briefly the detection of possible effects of the
regulatory changes that have been made in the structure of GEM, on the dynamic evolution of
SMP as it is reflected by its statistical properties or stylized effects. We have found that GEM has
the majority of stylized characteristics that other electricity markets exhibit and how these
compare with those in financial markets. We have given an in depth explanation of the sign and
the intensity of the impacts of both fundamental to the GEM factors as well as of the qualitative
or dummy variables constructed to capture the regulatory changes. We strongly believe that
our findings will contribute to efforts of the authorities entitled to make GEM more efficient and
competitive. Our results will be useful in better understanding of the factors of the underline
dynamics of SMP, an information needed both in restructuring GEM as well as in better
developing the forward market a requirement for compliance of GEM with the Target model.
We have not detected any leverage effects in GEM as other workers have found in other
markets (Karakatsani N., and Bunn,D.W., 2010), Bowden and Payne ,2008 , Knittel and Roberts,
2005 , Hadsell et al.,2004 ). Is this result explained by a lower degree of convexity of the supply
curve in GEM compared to higher degree of convexity in other markets, as Kanamura
(Kanamura , 2009) suggests?
Our findings enhances the results of Petrella et al. (2012) for the Italian market. We agree with
their remark that if an adequate number of similar works on other markets appear, then with
some degree of confidence, we could generalize our findings and state that changes in the
market architecture have indeed a significant effect on the dynamics of wholesale price.
A drawback of using dummy variables for the reforms is that the response of the market’s
agents to these stimuli is not smoothed but abrupt like a step function. Furthermore, if there is
a time lapse between the announcement of a reform and its implementation, this allows agents
in advance, to take advantage of the reforms by adjusting themselves according to their
position in the market.
We have not consider in this work, all possible interactions between different regulatory
reforms. A more detail analysis is needed in future work as suggested by a growing, recent and
focused on this topic, literature (child et.al, 2008).
Any required regulatory reforms that have to be applied, must be designed in such a way that
facilitate the gradual development of competitive environment, allowing at the same time the
minimization of the State’s intervention (in areas that this is necessary) to the market as well
as of the total cost of market transactions. The reforms also must create a secure environment
for all participants. For this reason, any reforms that have a transitional characteristic (as most
of the RMR considered in this study) must be evaluated according to the holistic or systemic
effects on the market due to their interdependence and the fact that they are inherently
coupled with the fundamental variables of the market, as the modeling results described in this
paper has revealed. The ultimate target, therefore, of any regulatory reform is to create motives
and signals to the agents of the market, so they have a collective movement to more
competitive behaviors and attitudes and suitable investment decisions. Towards this end, this
paper is believed to contribute to the current efforts of the Regulator and other relevant
market bodies, towards restructuring the market as well as in helping developing tools /
processes / rules etc., that will allow the fair pricing of product and service available in the
Greek Electricity market as well as in attracting investors in the market.
We also hope that the modeling results presented here can enhance the efforts of the reformers
of the GEM by helping them in detecting more accurately the factors of uncertainty, both
domestic and international, that influence heavily the Greek market and must be taken into
48
account when designing regulatory measures to face the continuously changing internal and
external environment.
However, we have to point out here that the phase out of any transitional mechanism without
first a detailed and in depth examination of the side effects this might have on the current
stability of the market, due to the strong interlinks and coupling nature these mechanisms have
with fundamental variables and have created all these years the current market microstructure,
may have an adverse impact on the available long term generation capacity. Care must be taken
therefore in securing future adequate availability by avoiding a forced canceling of mechanism
ready in place that may put in danger the current equilibrium in the market.
This means that the impact of the change in the method of calculating SMP in the Greek market
was extremely strong. It has completely change the structure of the underlying dynamicstochastic process of SMP i.e. its statistical properties or stylized facts, causing forcedly its
future dynamics evolution to be more volatile therefore more unpredictable. This regime
switching of the process from a stable or tranquil state to a new turbulent and unstable one,
give us an example of how an external perturbation (here a change in the regulatory
framework) to the stochastic system that describes SMP, no matter how small or large it is, can
cause the system to behave completely differently. This is a manifestation of nonlinearity and
sensitive dependence on initial conditions of the electricity market systems which are very
complex and nonlinear, requiring an extensive amount of simulations before attempting any
change on their structure.
Since an electricity market is a high dimensional setup (a high dimensional manifold on which
SMP is evolving, as referred in the jargon of Stochastic and Dynamical System theory) it is
natural to consider that all the distortions in the market as well as the history of external –
“exogenous” interventions in the market, is well incorporated in the dynamics of SMP, since this
variable is coupled, in a nonlinear – complex way, with the driving fundamental variables in the
market. Therefore, any movements in the explanatory variables used in modeling SMP
(including the regulatory reforms entered in the model as dummy variables), are well
“encapsulated” in the dynamics of SMP (Bask M., et. al, 2007, Broomhead D.S. et al, 1986,
Takens F., 1987, Serletis A., 2007). We have extracted both qualitative and quantitative
information from the SMP time series, that reveal how the factors have shaped its behavior and
at the same time, have generated as bi-products, the market’s structural frictions or
distortions.
Even though there is not an easy job to attribute to each separate market distortion a factor or a
combination of factors, due to the fact that, as we have said the system under examination is
high-dimensional, non-linear and (as a consequence) very complex, we consider that the
detected stylized facts of SMP, in our present analysis, can reveal an insight of the Market’s
distortions. Therefore, another question that is arising is whether the measures or policies of
the regulator mentioned above are the appropriate ones in a sense that they are capable of
removing permanently these distortions or of removing just the symptoms.
The combined effects on SMP of low demand (as in Greece due to economic crisis) and increase
generation by IPP´s were more intense in 2011 when two new CCGT plants were added and the
load reached very low levels. The effects on SMP were more apparent when IPP´s underwent
maintenance for some period (therefore Unit availability reduced) exerting an upward
movement on SMP.
As we have mentioned earlier a crucial prerequisite for GEM to be more efficient in the link
between wholesale (SMP) and retail prices. Therefore regulated prices must gradually be
adjusted, in order to eliminate cross-subsidy distortions and eventually produce retail prices
that reflect as close as possible wholesale market costs.
49
Disclaimer
The material in this work is for information, education, research and academic purposes only.
Any opinions, proposals and positions expressed in this paper are exclusively of the authors
and do not necessarily represent the views of ADMIE and CRANS, partially or unilaterally.
Acknowledgements
The Authors acknowledge the support of Mr. Evangelos Georgis of ADMIE S.A for his great
contribution to the paper, by providing to the authors with the raw and preprocessed data and
by participating in numerous discussions with the first of the authors on the intermediate and
final results. Thanks also to Mr. P Asslanis and A. Tsalpatouros, both of ADMIE S.A, for their help
in providing part of the data sets. Special thanks are given to Mrs. K. Armeni of ADMIE S.A for
the typing and general care of this manuscript.
50
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